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A109961
Expansion of (1-x)^3/(1-4x+5x^2-4x^3+x^4).
5
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.
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
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jul 06 2005
STATUS
approved