A050494 Partial sums of A051923.

1, 10, 52, 192, 570, 1452, 3300, 6864, 13299, 24310, 42328, 70720, 114036, 178296, 271320, 403104, 586245, 836418, 1172908, 1619200, 2203630, 2960100, 3928860, 5157360, 6701175, 8625006, 11003760, 13923712, 17483752, 21796720, 26990832, 33211200, 40621449

Offset: 0

Author

Barry E. Williams, Dec 26 1999

Keywords

• easy
• nonn

Comments

If Y is a 3-subset of an n-set X then, for n>=9, a(n-9) is the number of 9-subsets of X having at least two elements in common with Y. - Milan Janjic, Nov 23 2007

References

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

Links

• Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1)

Crossrefs

Cf. A051923.

Cf. A093560 ((3, 1) Pascal, column m=7).

Programs

Mathematica

Table[Binomial[n+6, 6]*(3*n+7)/7, {n, 0, 50}] (* Vladimir Joseph Stephan Orlovsky, Jan 27 2012 *)

Formula

a(n)=C(n+6, 6)*(3n+7)/7.

G.f.: (1+2*x)/(1-x)^8.