A114196 Expansion of (1-3x)/(1-6x+8x^2+x^3).

1, 3, 10, 35, 127, 472, 1781, 6783, 25978, 99823, 384331, 1481424, 5714073, 22048715, 85098282, 328485899, 1268080423, 4895497064, 18899853101, 72967061671, 281708048154, 1087611942455, 4199040207827, 16211637659168

Offset: 0

Author

Paul Barry, Nov 16 2005

Keywords

• easy
• nonn

Comments

Diagonal sums of A114195.

Links

• Index entries for linear recurrences with constant coefficients, signature (6, -8, -1).

Programs

Mathematica

CoefficientList[Series[(1-3x)/(1-6x+8x^2+x^3),{x,0,30}],x] (* or *) LinearRecurrence[{6,-8,-1},{1,3,10},30] (* Harvey P. Dale, Feb 02 2012 *)

Formula

a(n)=6a(n-1)-8a(n-2)-a(n-3); a(n)=sum{k=0..floor(n/2), sum{j=0..n-k, C(n-k, j)C(j+k, 2k)2^(j-k)}}.