

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
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OFFSET

0,1


COMMENTS

If Y is a 3subset of an nset X then, for n>=6, a(n6) is the number of 4subsets 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

Table of n, a(n) for n=0..39.


FORMULA

G.f.: (32*x)/(1x)^5.
a(n)= (n+12)*binomial(n+3, 3)/4 = 3*b(n)2*b(n1), with b(n):=binomial(n+4, 4); cf. A000332.
a(n) = sum_{k=1..n} ( sum_{i=1..k} i*(nk+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



