A339254 a(n) = 6*a(n - 1) - 12*a(n - 2) + 8*a(n - 3) for n >= 5, a(0) = 1, a(1) = 7, a(2) = 24, a(3) = 70, a(4) = 193.

1, 7, 24, 70, 193, 510, 1304, 3248, 7920, 18976, 44800, 104448, 240896, 550400, 1247232, 2805760, 6270976, 13934592, 30801920, 67764224, 148439040, 323878912, 704118784, 1525678080, 3295674368, 7098859520, 15250489344, 32682016768, 69877104640, 149082341376

Offset: 0

Author

Peter Luschny, Nov 29 2020

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-12,8).

Programs

Maple

a := proc(n) option remember; if n < 5 then return [1, 7, 24, 70, 193][n + 1] fi;
6*a(n - 1) - 12*a(n - 2) + 8*a(n - 3) end: seq(a(n), n = 0..29);

Mathematica

CoefficientList[Series[(5 x^4 + 2 x^3 - 6 x^2 + x + 1)/(1 - 2 x)^3, {x,0,29}], x]

Formula

a(n) = [x^n] (5*x^4 + 2*x^3 - 6*x^2 + x + 1) / (1 - 2*x)^3.

a(n) = n! [x^n] (exp(2*x)*(18*x^2 + 52*x + 35) - 10*x - 19)/16.

a(n) = 2^(n-5)*(70 + 43*n + 9*n^2) for n >= 2. - Stefano Spezia, Nov 29 2020