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A306847 a(n) = Sum_{k=0..floor(n/6)} binomial(n,6*k). 4
1, 1, 1, 1, 1, 1, 2, 8, 29, 85, 211, 463, 926, 1730, 3095, 5461, 9829, 18565, 37130, 77540, 164921, 349525, 728575, 1486675, 2973350, 5858126, 11450531, 22369621, 43942081, 87087001, 174174002, 350739488, 708653429, 1431655765, 2884834891, 5791193143 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,7

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..3000

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6).

FORMULA

G.f.: (1 - x)^5/((1 - x)^6 - x^6).

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) for n > 5.

a(n) = (4^n + (1 - t)^n + (1 + t)^n + (3 - t)^n + (3 + t)^n)/(6*2^n) for n > 0 and a(0) = 1, where t = i*sqrt(3) and i = sqrt(-1). - Bruno Berselli, Mar 13 2019

PROG

(PARI) {a(n) = sum(k=0, n\6, binomial(n, 6*k))}

(PARI) N=66; x='x+O('x^N); Vec((1-x)^5/((1-x)^6-x^6))

CROSSREFS

Column 6 of A306846.

Sequence in context: A061230 A241627 A293169 * A107025 A212385 A333882

Adjacent sequences:  A306844 A306845 A306846 * A306848 A306849 A306850

KEYWORD

nonn,easy

AUTHOR

Seiichi Manyama, Mar 13 2019

STATUS

approved

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Last modified June 4 06:41 EDT 2020. Contains 334822 sequences. (Running on oeis4.)