A369840 - OEIS

%I #19 Mar 15 2024 17:25:14

%S 1,1,2,7,23,68,194,555,1601,4633,13404,38752,112004,323728,935737,

%T 2704817,7818464,22599701,65325542,188826693,545813094,1577700612,

%U 4560424135,13182138184,38103641048,110140512968,318366757185,920255312908,2660044812499,7688994894381

%N Number of compositions of 5*n into parts 2 and 5.

%H Paolo Xausa, <a href="/A369840/b369840.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-9,10,-5,1).

%F a(n) = A001687(5*n+1).

%F a(n) = Sum_{k=0..floor(n/2)} binomial(n+3*k,n-2*k).

%F a(n) = 5*a(n-1) - 9*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).

%F G.f.: (1-x)^4/((1-x)^5 - x^2).

%F a(n) = A369843(n) - A369843(n-1). - _R. J. Mathar_, Feb 14 2024

%t LinearRecurrence[{5, -9, 10, -5, 1}, {1, 1, 2, 7, 23}, 50] (* _Paolo Xausa_, Mar 15 2024 *)

%o (PARI) a(n) = sum(k=0, n\2, binomial(n+3*k, n-2*k));

%Y Cf. A369803, A369842, A369843, A369844.

%Y Cf. A099131, A369836, A369845.

%Y Cf. A001687.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Feb 03 2024