A055799 T(2n+6,n), array T as in A055794.

1, 8, 37, 130, 385, 1012, 2431, 5434, 11440, 22880, 43758, 80444, 142766, 245480, 410210, 667964, 1062347, 1653608, 2523675, 3782350, 5574855, 8090940, 11575785, 16342950, 22789650, 31414656, 42839148, 57830872

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>=9, a(n-9) is the number of 9-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 (10,-45,120,-210,252,-210,120,-45,10,-1).

Crossrefs

Cf. A051601.

Programs

Magma

[Binomial(n,9)-2*Binomial(n-2,8):n in [9..40]]; // Vincenzo Librandi, May 01 2012

Mathematica

a=1;b=2;c=3;d=4;e=5;f=6;g=7;s=8;lst={1,s};Do[a+=n;b+=a;c+=b;d+=c;e+=d;f+=e;g+=f;s+=g;AppendTo[lst,s],{n,6!}];lst (* Vladimir Joseph Stephan Orlovsky, May 24 2009 *)
CoefficientList[Series[(1-2*x+2*x^2)/(1-x)^10,{x,0,30}],x] (* Vincenzo Librandi, May 01 2012 *)

Formula

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

G.f.: (1-2*x+2*x^2)/(1-x)^10. - Colin Barker, Feb 21 2012

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4)+ 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10). - Vincenzo Librandi, May 01 2012