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 A369842 #16 Mar 15 2024 11:09:30
%S A369842 1,3,7,18,52,154,450,1301,3753,10838,31327,90568,261813,756786,
%T A369842 2187496,6323023,18277014,52830706,152709940,441415867,1275934888,
%U A369842 3688154521,10660798289,30815580241,89074003241,257472939209,744238632362,2151259638423,6218325456983
%N A369842 Number of compositions of 5*n-1 into parts 2 and 5.
%H A369842 Paolo Xausa, <a href="/A369842/b369842.txt">Table of n, a(n) for n = 1..1000</a>
%H A369842 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-9,10,-5,1).
%F A369842 a(n) = A001687(5*n).
%F A369842 a(n) = Sum_{k=0..floor(n/2)} binomial(n+1+3*k,n-1-2*k).
%F A369842 a(n) = 5*a(n-1) - 9*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
%F A369842 G.f.: x*(1-x)^2/((1-x)^5 - x^2).
%t A369842 LinearRecurrence[{5, -9, 10, -5, 1}, {1, 3, 7, 18, 52}, 50] (* _Paolo Xausa_, Mar 15 2024 *)
%o A369842 (PARI) a(n) = sum(k=0, n\2, binomial(n+1+3*k, n-1-2*k));
%Y A369842 Cf. A369803, A369840, A369843, A369844.
%Y A369842 Cf. A001687.
%K A369842 nonn,easy
%O A369842 1,2
%A A369842 _Seiichi Manyama_, Feb 03 2024