This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A369813 #20 Dec 04 2024 14:56:58
%S A369813 1,0,1,0,1,0,1,1,1,2,1,3,1,4,2,5,4,6,7,7,11,9,16,13,22,20,29,31,38,47,
%T A369813 51,69,71,98,102,136,149,187,218,258,316,360,452,509,639,727,897,1043,
%U A369813 1257,1495,1766,2134,2493,3031,3536,4288,5031,6054,7165,8547,10196,12083,14484,17114,20538,24279,29085,34475
%N A369813 Expansion of 1/(1 - x^2 - x^7).
%C A369813 Number of compositions of n into parts 2 and 7.
%H A369813 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,0,0,0,1).
%F A369813 a(n) = a(n-2) + a(n-7).
%F A369813 a(n) = A007380(n-7) for n >= 8.
%t A369813 CoefficientList[Series[1/(1-x^2-x^7),{x,0,80}],x] (* or *) LinearRecurrence[{0,1,0,0,0,0,1},{1,0,1,0,1,0,1},80] (* _Harvey P. Dale_, Dec 04 2024 *)
%o A369813 (PARI) my(N=70, x='x+O('x^N)); Vec(1/(1-x^2-x^7))
%o A369813 (PARI) a(n) = sum(k=0, n\7, ((n-5*k)%2==0)*binomial((n-5*k)/2, k));
%Y A369813 Cf. A005709, A017847, A369814, A369815, A369816.
%Y A369813 Cf. A007380.
%K A369813 nonn,easy
%O A369813 0,10
%A A369813 _Seiichi Manyama_, Feb 02 2024