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A095661
Fifth column (m=4) of (1,3)-Pascal triangle A095660.
14
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
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]
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
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Jun 11 2004
STATUS
approved