A182260 Number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w

0, 3, 11, 28, 56, 99, 159, 240, 344, 475, 635, 828, 1056, 1323, 1631, 1984, 2384, 2835, 3339, 3900, 4520, 5203, 5951, 6768, 7656, 8619, 9659, 10780, 11984, 13275, 14655, 16128, 17696, 19363, 21131, 23004, 24984, 27075, 29279, 31600, 34040

Offset: 1

Author

Clark Kimberling, Apr 22 2012

Keywords

• nonn
• easy

Comments

Also the number of ordered triples (w,x,y) with all terms in {1,...,n} and 2w>x+y.

A182260(n)+A055232(n)=3^(n-1).

A182260 is row 1 of A211802 and also row 1 of A182259; see A211790 for a discussion and guide to related sequences.

Examples

			For n=2, the 3 triples (w,x,y) for which 2w<x+y are (1,1,2), (1,2,1), (1,2,2).  The 3 triples for which 2w>x+y are (2,1,1), (2,1,2), (2,2,1).
		

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).

Crossrefs

Cf. A211790, A211802.

Programs

Mathematica

(See the program at A211802.)
LinearRecurrence[{3,-2,-2,3,-1},{0,3,11,28,56},50] (* Harvey P. Dale, Aug 10 2019 *)

Formula

a(n) = 3*a(n-1)-2*a(n-2)-2*a(n-3)+3*a(n-4)-a(n-5).

From Colin Barker, May 06 2012: (Start)

a(n) = (-1+(-1)^n-2*n^2+4*n^3)/8.

G.f.: x^2*(3 + 2*x + x^2)/((1 - x)^4*(1 + x)). (End)