A055797 T(2n+4,n), array T as in A055794.

1, 6, 22, 64, 162, 372, 792, 1584, 3003, 5434, 9438, 15808, 25636, 40392, 62016, 93024, 136629, 196878, 278806, 388608, 533830, 723580, 968760, 1282320, 1679535, 2178306, 2799486, 3567232, 4509384

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>=7, a(n-7) is the number of 7-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
• Alexsandar Petojevic, The Function vM_m(s; a; z) and Some Well-Known Sequences, Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.7
• Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Crossrefs

Cf. A051601.

Programs

Magma

[Binomial(n,7) + Binomial(n,5): n in [5..40]]; // Vincenzo Librandi, May 01 2012

Maple

[seq(binomial(n,7)+binomial(n,5), n=5..34)]; # Zerinvary Lajos, Jul 24 2006

Mathematica

a=1;b=2;c=3;d=4;e=5;f=6;s=7;lst={s};Do[a+=n;b+=a;c+=b;d+=c;e+=d;f+=e;s+=f;AppendTo[lst,s],{n,6!}];lst (* Vladimir Joseph Stephan Orlovsky, May 24 2009 *)
CoefficientList[Series[(1-2*x+2*x^2)/(1-x)^8,{x,0,30}],x] (* Vincenzo Librandi, May 01 2012 *)
LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{1,6,22,64,162,372,792,1584},30] (* Harvey P. Dale, Mar 11 2023 *)

Formula

a(n-5) = binomial(n,7) + binomial(n,5) for n>4. - Zerinvary Lajos, Jul 24 2006

G.f.: (1-2*x+2*x^2)/(1-x)^8. - Colin Barker, Feb 22 2012

a(n) = 8*(n-1) - 28*(n-2) + 56*(n-3) - 70*(n-4) + 56*(n-5) - 28*(n-6) + 8*(n-7) - (n-8). - Vincenzo Librandi, May 01 2012

a(n) = (n+5)*(n+4)*(n+3)*(n+2)*(n+1)*(n^2-n+42)/5040. - R. J. Mathar, Oct 01 2021