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

0,2

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

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

Links

Kelvin Voskuijl, Table of n, a(n) for n = 0..10000

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

Formula

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

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

From Amiram Eldar, Nov 04 2025: (Start)

Sum_{n>=0} 1/a(n) = 5103*sqrt(3)*Pi/88 + 45927*log(3)/88 - 35511/40.

Sum_{n>=0} (-1)^n/a(n) = 5103*sqrt(3)*Pi/44 + 2688*log(2)/11 - 351799/440. (End)

E.g.f.: exp(x)*(5040 + 45360*x + 83160*x^2 + 54600*x^3 + 15750*x^4 + 2142*x^5 + 133*x^6 + 3*x^7)/5040. - Stefano Spezia, Mar 05 2026

Mathematica

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

Crossrefs

Cf. A051923.

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

Sequence in context: A257042 A092966 A281401 * A382675 A367460 A200035

Adjacent sequences: A050491 A050492 A050493 * A050495 A050496 A050497

Keyword

easy,nonn

Author

Barry E. Williams, Dec 26 1999

Status

approved