A099132 Quintisection of 1/(1-x^5-x^6).
1, 1, 1, 1, 1, 1, 2, 7, 22, 57, 127, 253, 464, 804, 1354, 2289, 4005, 7372, 14198, 28033, 55523, 108699, 208982, 394555, 734561, 1357136, 2504932, 4643816, 8671852, 16313856, 30855957, 58502733, 110882143, 209689343, 395358538, 743376838
Offset: 0
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..3646
- V. C. Harris, C. C. Styles, A generalization of Fibonacci numbers, Fib. Quart. 2 (1964) 277-289, sequence u(n,1,5).
- V. E. Hoggatt, Jr., 7-page typed letter to N. J. A. Sloane with suggestions for new sequences, circa 1977.
- Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1,1)
Programs
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Mathematica
LinearRecurrence[{5,-10,10,-5,1,1},{1,1,1,1,1,1},40] (* Harvey P. Dale, Aug 20 2012 *) -
PARI
Vec((1-x)^4/((1-x)^5-x^6) + O(x^40)) \\ Michel Marcus, Sep 06 2017
Formula
G.f.: (1-x)^4/((1-x)^5-x^6);
a(n) = Sum_{k=0..n} binomial(k, 5(n-k));
a(n) = 5a(n-1)-10a(n-2)+10a(n-3)-5a(n-4)+a(n-5)+a(n-6);
a(n) = A017837(5n).
a(n) = Sum_{k=0..floor(n/5)} binomial(n-k, 5k). - Paul Barry, May 09 2005