A055798 T(2n+5,n), array T as in A055794.

1, 7, 29, 93, 255, 627, 1419, 3003, 6006, 11440, 20878, 36686, 62322, 102714, 164730, 257754, 394383, 591261, 870067, 1258675, 1792505, 2516085, 3484845, 4767165, 6446700, 8625006, 11424492, 14991724, 19501108, 25158980, 32208132, 40932804, 51664173

Offset: 0

Author

Clark Kimberling, May 28 2000

Keywords

• nonn
• easy

Comments

If Y is a 2-subset of an n-set X then, for n>=8, a(n-8) is the number of 8-subsets of X which do not have exactly one element in common with Y. - Milan Janjic, Dec 28 2007

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Crossrefs

Cf. A051601.

Programs

Magma

[Binomial(n,8)-2*Binomial(n-2,7): n in [8..40]]; // Vincenzo Librandi, May 01 2012

Mathematica

CoefficientList[Series[(-2*(z - 1)*z - 1)/(z - 1)^9, {z, 0, 100}], z] (* Vladimir Joseph Stephan Orlovsky, Jul 16 2011 *)
LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{1,7,29,93,255,627,1419,3003,6006},50] (* Vincenzo Librandi, May 01 2012 *)

Formula

a(n-8) = binomial(n,8)-2*binomial(n-2,7), n=8,9,10,.... - Milan Janjic, Dec 28 2007

G.f.: (1-2*x+2*x^2)/(1-x)^9. [Colin Barker, Feb 22 2012]

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9). - Vincenzo Librandi, May 01 2012