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A306860 a(n) = Sum_{k=0..floor(n/9)} binomial(n,9*k). 4
1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 11, 56, 221, 716, 2003, 5006, 11441, 24311, 48622, 92398, 168151, 295261, 504736, 850840, 1442101, 2523676, 4686826, 9373652, 20030039, 44612702, 100804436, 226444616, 499685777, 1076832989, 2261792303, 4631710931, 9263421862 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,10

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,2).

FORMULA

G.f.: (1 - x)^8/((1 - x)^9 - x^9).

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + 2*a(n-9) for n > 8.

PROG

(PARI) {a(n) = sum(k=0, n\9, binomial(n, 9*k))}

(PARI) N=66; x='x+O('x^N); Vec((1-x)^8/((1-x)^9-x^9))

CROSSREFS

Column 9 of A306846.

Sequence in context: A221019 A115205 A306753 * A212388 A198769 A037554

Adjacent sequences:  A306857 A306858 A306859 * A306861 A306862 A306863

KEYWORD

nonn,easy

AUTHOR

Seiichi Manyama, Mar 14 2019

STATUS

approved

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Last modified May 31 21:59 EDT 2020. Contains 334754 sequences. (Running on oeis4.)