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A306852
a(n) = Sum_{k=0..floor(n/7)} binomial(n,7*k).
3
1, 1, 1, 1, 1, 1, 1, 2, 9, 37, 121, 331, 793, 1717, 3434, 6451, 11561, 20129, 34885, 62017, 116281, 232562, 490337, 1062601, 2309385, 4950751, 10381281, 21242341, 42484682, 83411715, 161766061, 312168761, 603861897, 1178135905, 2326683921, 4653367842
OFFSET
0,8
FORMULA
G.f.: (1 - x)^6/((1 - x)^7 - x^7).
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + 2*a(n-7) for n > 6.
MATHEMATICA
a[n_] := Sum[Binomial[n, 7*k], {k, 0, Floor[n/7]}]; Array[a, 36, 0] (* Amiram Eldar, May 25 2021 *)
PROG
(PARI) {a(n) = sum(k=0, n\7, binomial(n, 7*k))}
(PARI) N=66; x='x+O('x^N); Vec((1-x)^6/((1-x)^7-x^7))
CROSSREFS
Column 7 of A306846.
Sequence in context: A330346 A280351 A306721 * A275425 A373912 A212386
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Mar 14 2019
STATUS
approved