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Number of compositions of 6*n-3 into parts 5 and 6.
3

%I #11 Jun 24 2024 08:47:16

%S 0,0,1,4,10,20,35,57,94,175,385,935,2289,5385,12031,25686,53176,

%T 108699,223215,465867,991088,2138884,4643816,10067197,21695156,

%U 46427790,98807200,209689343,444983081,946084386,2016738335,4308708305,9217134511,19720875625

%N Number of compositions of 6*n-3 into parts 5 and 6.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,7,-1).

%F a(n) = A017837(6*n-3).

%F a(n) = Sum_{k=0..floor(n/5)} binomial(n+k,n-3-5*k).

%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 7*a(n-5) - a(n-6).

%F G.f.: x^3*(1-x)^2/((1-x)^6 - x^5).

%F a(n) = A373964(n+1) - A373964(n).

%o (PARI) a(n) = sum(k=0, n\5, binomial(n+k, n-3-5*k));

%Y Cf. A107025, A369794, A373961, A373962, A373964.

%Y Cf. A017837.

%K nonn,easy

%O 1,4

%A _Seiichi Manyama_, Jun 24 2024