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%I #28 May 26 2021 00:54:54
%S 1,1,1,1,1,1,1,2,9,37,121,331,793,1717,3434,6451,11561,20129,34885,
%T 62017,116281,232562,490337,1062601,2309385,4950751,10381281,21242341,
%U 42484682,83411715,161766061,312168761,603861897,1178135905,2326683921,4653367842
%N a(n) = Sum_{k=0..floor(n/7)} binomial(n,7*k).
%H Seiichi Manyama, <a href="/A306852/b306852.txt">Table of n, a(n) for n = 0..3000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,2).
%F G.f.: (1 - x)^6/((1 - x)^7 - x^7).
%F 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.
%t a[n_] := Sum[Binomial[n,7*k], {k,0,Floor[n/7]}]; Array[a, 36, 0] (* _Amiram Eldar_, May 25 2021 *)
%o (PARI) {a(n) = sum(k=0, n\7, binomial(n, 7*k))}
%o (PARI) N=66; x='x+O('x^N); Vec((1-x)^6/((1-x)^7-x^7))
%Y Column 7 of A306846.
%K nonn,easy
%O 0,8
%A _Seiichi Manyama_, Mar 14 2019
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