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

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

1,2

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.

Links

Table of n, a(n) for n=1..41.

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

Formula

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

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)). [Colin Barker, May 06 2012]

Example

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).

Mathematica

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

Crossrefs

Cf. A211790, A211802.

Sequence in context: A210611 A119074 A211810 * A163696 A092781 A332669

Adjacent sequences: A182257 A182258 A182259 * A182261 A182262 A182263

Keyword

nonn,easy

Author

Clark Kimberling, Apr 22 2012

Status

approved