A124370 Expansion of 1/(1-2x^2-3x^3-x^4).
1, 0, 2, 3, 5, 12, 21, 42, 83, 159, 313, 609, 1186, 2316, 4512, 8799, 17158, 33450, 65225, 127173, 247958, 483471, 942660, 1837989, 3583691, 6987429, 13624009, 26563920, 51793996, 100987296, 196903761, 383920500
Offset: 0
Links
- Harvey P. Dale, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (0,2,3,1).
Programs
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Mathematica
CoefficientList[Series[1/(1-2x^2-3x^3-x^4),{x,0,40}],x] (* or *) LinearRecurrence[{0,2,3,1},{1,0,2,3},40] (* Harvey P. Dale, Feb 11 2015 *)
Formula
a(n)=sum{k=0..floor(n/2), sum{j=0..n-k, C(j,n-k-j)*C((j+k)/2,(j-k)/2)*(1+(-1)^(j-k))/2}}
a(0)=1, a(1)=0, a(2)=2, a(3)=3, a(n)=2*a(n-2)+3*a(n-3)+a(n-4). - Harvey P. Dale, Feb 11 2015
Comments