A202012 Expansion of (1-x+x^2)/((1-x)(1-x-x^2-x^3)).

1, 1, 3, 6, 11, 21, 39, 72, 133, 245, 451, 830, 1527, 2809, 5167, 9504, 17481, 32153, 59139, 108774, 200067, 367981, 676823, 1244872, 2289677, 4211373, 7745923, 14246974, 26204271, 48197169, 88648415, 163049856

Offset: 0

Author

Philippe Deléham, Dec 08 2011

Keywords

• easy
• nonn

Comments

Antidiagonal sums of triangle T(n,k) = A104040(n,k)*(-1)^floor(k/2). - Philippe Deléham, Dec 11 2011

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,0,0,-1).

Crossrefs

Cf. A008937, A081172, A104040.

Programs

Mathematica

CoefficientList[Series[(1-x+x^2)/((1-x)(1-x-x^2-x^3)),{x,0,40}],x] (* or *) LinearRecurrence[{2,0,0,-1},{1,1,3,6},40] (* Harvey P. Dale, Apr 21 2014 *)

Formula

a(n) = 2*a(n-1) - a(n-4), n>3.

a(n) = A008937(n-1) - A008937(n) + A008937(n+1). - R. J. Mathar, Dec 10 2011

a(n+1)-a(n) = A081172(n+2). - Philippe Deléham, Dec 11 2011