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%I #13 Mar 15 2024 05:37:00
%S 1,1,1,1,1,1,1,2,5,11,21,36,57,85,122,173,249,371,575,918,1485,2398,
%T 3830,6030,9369,14422,22107,33909,52226,80888,125925,196706,307653,
%U 480873,750275,1168085,1815191,2817518,4371772,6785606,10539893,16384908,25488736
%N a(n) = Sum_{k=0..floor(n/7)} binomial(n-4*k,3*k).
%H Paolo Xausa, <a href="/A370722/b370722.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1,0,0,0,1).
%F G.f.: (1-x)^2/((1-x)^3 - x^7).
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-7).
%t LinearRecurrence[{3, -3, 1, 0, 0, 0, 1}, Table[1, 7], 50] (* _Paolo Xausa_, Mar 15 2024 *)
%o (PARI) a(n) = sum(k=0, n\7, binomial(n-4*k, 3*k));
%o (PARI) my(N=50, x='x+O('x^N)); Vec((1-x)^2/((1-x)^3-x^7))
%Y Cf. A003522, A100134, A137356.
%Y Cf. A003520, A005689, A348289.
%K nonn,easy
%O 0,8
%A _Seiichi Manyama_, Feb 28 2024