Download Applications of Fibonacci Numbers: Volume 6 Proceedings of by Peter G. Anderson (auth.), Professor Gerald E. Bergum, PDF

By Peter G. Anderson (auth.), Professor Gerald E. Bergum, Professor Andreas N. Philippou, Professor Alwyn F. Horadam (eds.)

ISBN-10: 9401065837

ISBN-13: 9789401065832

This booklet includes forty three papers shape one of the fifty five papers offered on the 6th foreign convention on Fibonacci Numbers and Their functions which was once held at Washington country college, Pullman, Washington, from July 18-22, 1994. those papers were chosen after a cautious overview via popular referees within the box, they usually variety from uncomplicated quantity conception to chance and records. The Fibonacci numbers and recurrence relatives are their unifying bond. it truly is expected that this e-book, like its 5 predecessors, should be valuable to analyze staff and graduate scholars attracted to the Fibonacci numbers and their functions. October 30, 1995 The Editors Gerald E. Bergum South Dakota kingdom college Brookings, South Dakota, U.S.A. Alwyn F. Horadam college of recent England Armidale, N.S.W., Australia Andreas N. Philippou 26 Atlantis highway Aglangia, Nicosia Cyprus xxi THE ORGANIZING COMMITTEES neighborhood COMMITTEE overseas COMMITTEE lengthy, Calvin T., Co-Chair Horadam, A.F. (Australia), Co-Chair Webb, William A., Co-Chair Philippou, A.N. (Cyprus), Co-Chair Burke, John Ando, S. (Japan) DeTemple, Duane W.

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Read or Download Applications of Fibonacci Numbers: Volume 6 Proceedings of ‘The Sixth International Research Conference on Fibonacci Numbers and Their Applications’, Washington State University, Pullman, Washington, U.S.A., July 18–22, 1994 PDF

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Extra info for Applications of Fibonacci Numbers: Volume 6 Proceedings of ‘The Sixth International Research Conference on Fibonacci Numbers and Their Applications’, Washington State University, Pullman, Washington, U.S.A., July 18–22, 1994

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This is a special case of the generalized Pascal's triangle defined by a strong divisibility sequence {An}. A strong divisibility sequence is a sequence {An} satisfying GCD(A m, An) = A. where 8 =GCD(m,n). Replacing n! in the definition of binomial coefficient by the product Al A 2 A 3 ••• A n for a strong divisibility sequence, we can obtain many other generalizations of Pascal's triangle. Ando's modification of Pascal's triangle uses the denominator of Leibnitz coefficients in place of binomial coefficients.

An alternative, and simpler, construction, based on Method 2, Eq. (27), is to specify the mask as M[i][j] = (iG n + jGn +1)%Gn + 2 (28) This mask is definitely meant to be developed "on the fly"; that is, the values M[i][j] can be computed as needed rather than pre-computed and stored; the computing effort is no more than the cost of subscripting. See Table 1 for the 19-1evel mask. The halftoned images Figs. 5-10 were generated using this Method 2. Whichever method is used to form a dithering mask, we recommend the parameters, GIg = 595, G 21 = 1278, and G 22 = 1873.

F. Horadam. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1991, pp. 9-16. [3] Ando, S. and Sato, D. " Applications ill Fibonacci Numbers, Volume 5. E. N. F. Horadam. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1993, pp. 37-43. MULTIPLE COLOR VERSION OF THE STAR OF DAVID THEOREMS ON PASCAL'S TRIANGLE AND RELATED ARRAYS OF NUMBERS Shiro Ando and Daihachiro Sato 1. INTRODUCTION (TWO AND THREE COLOR THEOREMS) This paper deals with research results which are a continuation of the reports given in [2], [3], [8], [10] and [11].

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