

A099132


Quintisection of 1/(1x^5x^6).


1



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
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OFFSET

0,7


LINKS

Table of n, a(n) for n=0..35.
V. C. Harris, C. C. Styles, A generalization of Fibonacci numbers, Fib. Quart. 2 (1964) 277289, sequence u(n,1,5).
V. E. Hoggatt, Jr., 7page 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)


FORMULA

G.f.: (1x)^4/((1x)^5x^6);
a(n) = Sum_{k=0..n} binomial(k, 5(nk));
a(n) = 5a(n1)10a(n2)+10a(n3)5a(n4)+a(n5)+a(n6);
a(n) = A017837(5n).
a(n) = Sum_{k=0..floor(n/5)} binomial(nk, 5k).  Paul Barry, May 09 2005


MATHEMATICA

LinearRecurrence[{5, 10, 10, 5, 1, 1}, {1, 1, 1, 1, 1, 1}, 40] (* Harvey P. Dale, Aug 20 2012 *)


PROG

(PARI) Vec((1x)^4/((1x)^5x^6) + O(x^40)) \\ Michel Marcus, Sep 06 2017


CROSSREFS

Cf. A005676.
Sequence in context: A153564 A153527 A153556 * A139398 A226910 A275423
Adjacent sequences: A099129 A099130 A099131 * A099133 A099134 A099135


KEYWORD

easy,nonn


AUTHOR

Paul Barry, Sep 29 2004


STATUS

approved



