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 A095661 Fifth column (m=4) of (1,3)-Pascal triangle A095660. 13
 3, 13, 35, 75, 140, 238, 378, 570, 825, 1155, 1573, 2093, 2730, 3500, 4420, 5508, 6783, 8265, 9975, 11935, 14168, 16698, 19550, 22750, 26325, 30303, 34713, 39585, 44950, 50840, 57288, 64328, 71995, 80325, 89355, 99123, 109668, 121030, 133250, 146370 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 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 Row 3 of the convolution array A213550. [Clark Kimberling, Jun 20 2012] LINKS FORMULA G.f.: (3-2*x)/(1-x)^5. 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. a(n) = sum_{k=1..n} ( sum_{i=1..k} i*(n-k+3) ), with offset 1. - Wesley Ivan Hurt, Sep 25 2013 MAPLE A095661:=n->(n+12)*binomial(n+3, 3)/4; seq(A095661(k), k=0..50); # Wesley Ivan Hurt, Oct 10 2013 MATHEMATICA 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 *) Table[(n+12)Binomial[n+3, 3)/4, {n, 0, 50}] (* Wesley Ivan Hurt, Oct 10 2013 *) CROSSREFS Partial sums of A006503. Sequence in context: A154154 A281868 A137976 * A058214 A108480 A322187 Adjacent sequences:  A095658 A095659 A095660 * A095662 A095663 A095664 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Jun 11 2004 STATUS approved

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Last modified December 4 12:45 EST 2020. Contains 338923 sequences. (Running on oeis4.)