A109961 Expansion of (1-x)^3/(1-4x+5x^2-4x^3+x^4).

1, 1, 2, 6, 17, 45, 117, 305, 798, 2090, 5473, 14329, 37513, 98209, 257114, 673134, 1762289, 4613733, 12078909, 31622993, 82790070, 216747218, 567451585, 1485607537, 3889371025, 10182505537, 26658145586, 69791931222, 182717648081

Offset

0,3

Comments

Diagonal sums of number triangle A109960.

Links

Table of n, a(n) for n=0..28.

Index entries for linear recurrences with constant coefficients, signature (4,-5,4,-1).

Formula

a(n)=sum{k=0..floor(n/2), binomial(n+2k, 4k)}.

a(0)=1, a(1)=1, a(2)=2, a(3)=6, a(n)=4*a(n-1)-5*a(n-2)+4*a(n-3)-a(n-4). - Harvey P. Dale, Dec 11 2013

Mathematica

CoefficientList[Series[(1-3x+3x^2-x^3)/(1-4x+5x^2-4x^3+x^4), {x, 0, 40}], x] (* or *) LinearRecurrence[{4, -5, 4, -1}, {1, 1, 2, 6}, 40] (* Harvey P. Dale, Dec 11 2013 *)

Crossrefs

Sequence in context: A309757 A020963 A065068 * A288029 A268655 A350431

Adjacent sequences: A109958 A109959 A109960 * A109962 A109963 A109964

Keyword

easy,nonn

Author

Paul Barry, Jul 06 2005

Status

approved