A095661 - OEIS

%I #22 Aug 27 2014 06:23:33

%S 3,13,35,75,140,238,378,570,825,1155,1573,2093,2730,3500,4420,5508,

%T 6783,8265,9975,11935,14168,16698,19550,22750,26325,30303,34713,39585,

%U 44950,50840,57288,64328,71995,80325,89355,99123,109668,121030,133250,146370

%N Fifth column (m=4) of (1,3)-Pascal triangle A095660.

%C 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 Row 3 of the convolution array A213550. [_Clark Kimberling_, Jun 20 2012]

%F G.f.: (3-2*x)/(1-x)^5.

%F 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 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:=n->(n+12)*binomial(n+3, 3)/4; seq(A095661(k), k=0..50); # _Wesley Ivan Hurt_, Oct 10 2013

%t 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 Table[(n+12)Binomial[n+3, 3)/4, {n, 0, 50}] (* _Wesley Ivan Hurt_, Oct 10 2013 *)

%Y Partial sums of A006503.

%K nonn,easy

%O 0,1

%A _Wolfdieter Lang_, Jun 11 2004