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 A095661 #27 Jun 05 2025 06:34:32
%S A095661 3,13,35,75,140,238,378,570,825,1155,1573,2093,2730,3500,4420,5508,
%T A095661 6783,8265,9975,11935,14168,16698,19550,22750,26325,30303,34713,39585,
%U A095661 44950,50840,57288,64328,71995,80325,89355,99123,109668,121030,133250,146370
%N A095661 Fifth column (m=4) of (1,3)-Pascal triangle A095660.
%C A095661 If Y is a 3-subset of an n-set X then, for n>=6, a(n-6) is the number of 4-subsets of X having at most one element in common with Y. - _Milan Janjic_, Nov 23 2007
%C A095661 Row 3 of the convolution array A213550. - _Clark Kimberling_, Jun 20 2012
%F A095661 G.f.: (3-2*x)/(1-x)^5.
%F A095661 a(n) = (n+12)*binomial(n+3, 3)/4 = 3*b(n)-2*b(n-1), with b(n) := binomial(n+4, 4); cf. A000332.
%F A095661 a(n) = Sum_{k=1..n} Sum_{i=1..k} i*(n-k+3), with offset 1. - _Wesley Ivan Hurt_, Sep 25 2013
%p A095661 A095661:=n->(n+12)*binomial(n+3, 3)/4; seq(A095661(k), k=0..50); # _Wesley Ivan Hurt_, Oct 10 2013
%t A095661 s1=s2=s3=s4=0;lst={};Do[a=n+(n+2);s1+=a;s2+=s1;s3+=s2;s4+=s3;AppendTo[lst,s3/2],{n,2,5!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Apr 04 2009 *)
%t A095661 Table[(n+12)Binomial[n+3, 3]/4, {n, 0, 50}] (* _Wesley Ivan Hurt_, Oct 10 2013 *)
%Y A095661 Partial sums of A006503.
%Y A095661 Cf. A213550.
%K A095661 nonn,easy
%O A095661 0,1
%A A095661 _Wolfdieter Lang_, Jun 11 2004