%I #16 Mar 15 2024 11:23:31
%S 0,1,4,10,21,44,101,250,629,1557,3784,9120,21992,53228,129177,313701,
%T 761403,1846804,4478044,10858285,26332515,63865592,154900529,
%U 375691009,911166977,2209835169,5359470121,12998281146,31524747503,76457088518,185431544730
%N Number of compositions of 5*n-1 into parts 3 and 5.
%H Paolo Xausa, <a href="/A369846/b369846.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,11,-5,1).
%F a(n) = A052920(5*n-1).
%F a(n) = Sum_{k=0..floor(n/3)} binomial(n+1+2*k,n-2-3*k).
%F a(n) = 5*a(n-1) - 10*a(n-2) + 11*a(n-3) - 5*a(n-4) + a(n-5).
%F G.f.: x^2*(1-x)/((1-x)^5 - x^3).
%t LinearRecurrence[{5, -10, 11, -5, 1}, {0, 1, 4, 10, 21}, 50] (* _Paolo Xausa_, Mar 15 2024 *)
%o (PARI) a(n) = sum(k=0, n\3, binomial(n+1+2*k, n-2-3*k));
%Y Cf. A369804, A369845, A369847, A369848.
%Y Cf. A052920.
%K nonn,easy
%O 1,3
%A _Seiichi Manyama_, Feb 03 2024
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