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A051923 Partial sums of A051836. 8
1, 9, 42, 140, 378, 882, 1848, 3564, 6435, 11011, 18018, 28392, 43316, 64260, 93024, 131784, 183141, 250173, 336490, 446292, 584430, 756470, 968760, 1228500, 1543815, 1923831, 2378754, 2919952, 3560040, 4312968, 5194112, 6220368, 7410249, 8783985, 10363626 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

If Y is a 3-subset of an n-set X then, for n>=8, a(n-8) is the number of 8-subsets of X having at least two elements in common with Y. - Milan Janjic, Nov 23 2007

a(n) is the n-th antidiagonal sum of the convolution array A213551. [Clark Kimberling, Jun 17 2012]

REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

Herbert John Ryser, Combinatorial Mathematics, "The Carus Mathematical Monographs", No. 14, John Wiley and Sons, 1963, pps. 1-8.

LINKS

Table of n, a(n) for n=0..34.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

FORMULA

a(n) = C(n+5, 5)*(n+2)/2.

G.f.: (1+2*x)/(1-x)^7.

a(n) = sum( k*A000217(k)*A000217(n-k+2), k=1..n+1). [Bruno Berselli, Sep 04 2013]

EXAMPLE

From the third formula: a(4) = 15+60+108+120+75 = 378. [Bruno Berselli, Sep 04 2013]

MATHEMATICA

CoefficientList[Series[(1 + 2 x)/(1 - x)^7, {x, 0, 25}], x]  (* Harvey P. Dale, Mar 13 2011 *)

Nest[Accumulate, Range[1, 120, 3], 5] (* Vladimir Joseph Stephan Orlovsky, Jan 28 2012 *)

CROSSREFS

Cf. A000217, A027801, A051836.

Cf. A093560 ((3, 1) Pascal, column m=6).

Sequence in context: A000971 A061927 A292481 * A180670 A268262 A293101

Adjacent sequences:  A051920 A051921 A051922 * A051924 A051925 A051926

KEYWORD

nonn,easy

AUTHOR

Barry E. Williams, Dec 19 1999

STATUS

approved

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Last modified October 20 07:17 EDT 2018. Contains 316378 sequences. (Running on oeis4.)