A144499 Column 3 of array in A144502.

1, 16, 155, 1633, 19714, 272501, 4269271, 74971240, 1460701853, 31295474659, 731658123646, 18541725927671, 506405138998225, 14830681754924608, 463675143369795659, 15415347314972132761, 543080592733655070466, 20211128647048824421085, 792340775489805581958823

Offset: 0

Author

David Applegate and N. J. A. Sloane, Dec 13 2008

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..402

Crossrefs

Cf. A144502.

Programs

Magma

[n le 2 select (16)^(n-1) else ((12*(n-1)^2+8*(n-1)+3)*Self(n-1) + (6*(n-1)+1)*Self(n-2) )/(6*(n-1) -5): n in [1..30]]; // G. C. Greubel, Oct 07 2023

Mathematica

a[n_]:= a[n]= If[n<2, 16^n, ((12*n^2+8*n+3)*a[n-1] +(6*n+1)*a[n-2])/(6*n-5)];
Table[a[n], {n, 0, 30}] (* G. C. Greubel, Oct 07 2023 *)

SageMath

@CachedFunction
def a(n): # a = A144499
    if n<2: return (16)^n
    else: return ((12*n^2+8*n+3)*a(n-1) +(6*n+1)*a(n-2))/(6*n-5)
[a(n) for n in range(31)] # G. C. Greubel, Oct 07 2023

Formula

(6*n-5)*a(n) = (12*n^2 +8*n +3)*a(n-1) + (6*n+1)*a(n-2). - G. C. Greubel, Oct 07 2023