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A095667
Fifth column (m=4) of (1,4)-Pascal triangle A095666.
5
4, 17, 45, 95, 175, 294, 462, 690, 990, 1375, 1859, 2457, 3185, 4060, 5100, 6324, 7752, 9405, 11305, 13475, 15939, 18722, 21850, 25350, 29250, 33579, 38367, 43645, 49445, 55800, 62744, 70312, 78540, 87465, 97125, 107559, 118807, 130910, 143910, 157850
OFFSET
0,1
COMMENTS
If Y is a 4-subset of an n-set X then, for n>=7, a(n-7) is the number of 4-subsets of X having at most one element in common with Y. - Milan Janjic, Dec 08 2007
In this sequence if we do a forward difference, then the 3rd forward difference when considered as a sequence will be an arithmetic progression with common difference 1. The same way the sequence formed by the 3rd forward difference of A047668 will be an arithmetic progression with common difference 8. [From Gopalakrishnan (gopala498(AT)yahoo.co.in), Jun 05 2010]
Row 4 of the convolution array A213550. [Clark Kimberling, Jun 20 2012]
FORMULA
G.f.: (4-3*x)/(1-x)^5.
a(n) = 4*b(n)-3*b(n-1) = (n+16)*binomial(n+3, 3)/4, with b(n):=binomial(n+4, 4)= A000332(n+4, 4).
a(n) = sum_{k=1..n} ( sum_{i=1..k} i*(n-k+4) ). - Wesley Ivan Hurt, Sep 25 2013
MAPLE
A095667:=n->(n+16)*binomial(n+3, 3)/4; seq(A095667(k), k=0..70); # Wesley Ivan Hurt, Sep 25 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, 3, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Apr 04 2009 *)
CROSSREFS
Partial sums of A060488.
Sequence in context: A166781 A376232 A147656 * A212577 A332863 A119949
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Jun 11 2004
STATUS
approved