A055809 a(n) = T(n,n-4), array T as in A055807.

1, 15, 32, 56, 88, 129, 180, 242, 316, 403, 504, 620, 752, 901, 1068, 1254, 1460, 1687, 1936, 2208, 2504, 2825, 3172, 3546, 3948, 4379, 4840, 5332, 5856, 6413, 7004, 7630, 8292, 8991, 9728, 10504, 11320, 12177, 13076

Offset: 4

Author

Clark Kimberling, May 28 2000

Keywords

• nonn
• easy

Comments

If Y_i (i=1,2,3,4) are 2-blocks of an n-set X then, for n>=8, a(n-2) is the number of (n-3)-subsets of X intersecting each Y_i (i=1,2,3,4). - Milan Janjic, Nov 09 2007

Links

• G. C. Greubel, Table of n, a(n) for n = 4..1000
• Milan Janjic, Two Enumerative Functions
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A055807, A055810, A055811, A055815, A055816, A055817.

Programs

GAP

Concatenation([1], List([5..50], n-> n*(n^2 +3*n -22)/6 )); # G. C. Greubel, Jan 23 2020

Magma

[1] cat [n*(n^2 +3*n -22)/6: n in [5..50]]; // G. C. Greubel, Jan 23 2020

Maple

seq( `if`(n=4, 1, n*(n^2 +3*n -22)/6), n=4..50); # G. C. Greubel, Jan 23 2020

Mathematica

f[n_]:=Sum[i+i^2-8,{i,1,n}]/2;Table[f[n],{n,5,5!}] (* Vladimir Joseph Stephan Orlovsky, Mar 08 2010 *)
Table[If[n==4, 1, n*(n^2 +3*n -22)/6], {n,4,50}] (* G. C. Greubel, Jan 23 2020 *)

PARI

Vec(x^4*(1 + 11*x - 22*x^2 + 14*x^3 - 3*x^4)/(1-x)^4 + O(x^50)) \\ Michel Marcus, Jan 10 2015

PARI

vector(50, n, my(m=n+3); if(m==4, 1, m*(m^2 +3*m -22)/6)) \\ G. C. Greubel, Jan 23 2020

Sage

[1]+[n*(n^2 +3*n -22)/6 for n in (5..50)] # G. C. Greubel, Jan 23 2020

Formula

For n>4, a(n) = n*(n^2 + 3*n - 22)/6.

G.f.: x^4*(1 + 11*x - 22*x^2 + 14*x^3 - 3*x^4)/(1-x)^4. - Colin Barker, Feb 22 2012

E.g.f.: x*(72 +48*x +8*x^2 -3*x^2 + (-72 +24*x +4*x^2)*exp(x))/24. - G. C. Greubel, Jan 23 2020