cp's OEIS Frontend

A369840 Number of compositions of 5*n into parts 2 and 5.

%I A369840 #19 Mar 15 2024 17:25:14
%S A369840 1,1,2,7,23,68,194,555,1601,4633,13404,38752,112004,323728,935737,
%T A369840 2704817,7818464,22599701,65325542,188826693,545813094,1577700612,
%U A369840 4560424135,13182138184,38103641048,110140512968,318366757185,920255312908,2660044812499,7688994894381
%N A369840 Number of compositions of 5*n into parts 2 and 5.
%H A369840 Paolo Xausa, <a href="/A369840/b369840.txt">Table of n, a(n) for n = 0..1000</a>
%H A369840 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-9,10,-5,1).
%F A369840 a(n) = A001687(5*n+1).
%F A369840 a(n) = Sum_{k=0..floor(n/2)} binomial(n+3*k,n-2*k).
%F A369840 a(n) = 5*a(n-1) - 9*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
%F A369840 G.f.: (1-x)^4/((1-x)^5 - x^2).
%F A369840 a(n) = A369843(n) - A369843(n-1). - _R. J. Mathar_, Feb 14 2024
%t A369840 LinearRecurrence[{5, -9, 10, -5, 1}, {1, 1, 2, 7, 23}, 50] (* _Paolo Xausa_, Mar 15 2024 *)
%o A369840 (PARI) a(n) = sum(k=0, n\2, binomial(n+3*k, n-2*k));
%Y A369840 Cf. A369803, A369842, A369843, A369844.
%Y A369840 Cf. A099131, A369836, A369845.
%Y A369840 Cf. A001687.
%K A369840 nonn
%O A369840 0,3
%A A369840 _Seiichi Manyama_, Feb 03 2024