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 A095667 Fifth column (m=4) of (1,4)-Pascal triangle A095666. 4
 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 (list; graph; refs; listen; history; text; internal format)
 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] LINKS 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: A162148 A166781 A147656 * A212577 A332863 A119949 Adjacent sequences:  A095664 A095665 A095666 * A095668 A095669 A095670 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Jun 11 2004 STATUS approved

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Last modified May 17 22:15 EDT 2021. Contains 343992 sequences. (Running on oeis4.)