A055796 T(2n+3,n), array T as in A055794.

1, 5, 16, 42, 98, 210, 420, 792, 1419, 2431, 4004, 6370, 9828, 14756, 21624, 31008, 43605, 60249, 81928, 109802, 145222, 189750, 245180, 313560, 397215, 498771, 621180, 767746, 942152, 1148488, 1391280, 1675520, 2006697, 2390829, 2834496, 3344874, 3929770

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>=6, a(n-6) is the number of 6-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 (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A051601.

Programs

Magma

[(n+1)*(n+2)*(n+3)*(n+4)*(n^2-n+30)/720: n in [0..40]]; // Vincenzo Librandi, Apr 30 2012

Maple

seq(binomial(n+4, 6)+binomial(n+4, 4), n=0..33) # Zerinvary Lajos, Jul 24 2006

Mathematica

a=1;b=2;c=3;d=4;s=5;lst={1,s};Do[a+=n;b+=a;c+=b;d+=c;s+=d;AppendTo[lst,s],{n,6!}];lst (* Vladimir Joseph Stephan Orlovsky, May 24 2009 *)
LinearRecurrence[{7,-21,35,-35,21,-7,1},{1,5,16,42,98, 210,420},50] (* Vincenzo Librandi, Apr 30 2012 *)
Table[(n+1)(n+2)(n+3)(n+4)(n^2-n+30)/720,{n,0,50}] (* Harvey P. Dale, Feb 12 2013 *)

Formula

a(n) = (n+1)(n+2)(n+3)(n+4)(n^2-n+30)/720.

a(n-4) = binomial(n,6) + binomial(n,4) for n>3. - Zerinvary Lajos, Jul 24 2006

G.f.: (1-2*x+2*x^2)/(1-x)^7. - Colin Barker, Feb 22 2012

Extensions

More terms from Harvey P. Dale, Feb 12 2013