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A144499
Column 3 of array in A144502.
6
1, 16, 155, 1633, 19714, 272501, 4269271, 74971240, 1460701853, 31295474659, 731658123646, 18541725927671, 506405138998225, 14830681754924608, 463675143369795659, 15415347314972132761, 543080592733655070466, 20211128647048824421085, 792340775489805581958823
OFFSET
0,2
LINKS
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
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 *)
PROG
(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
(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
CROSSREFS
Cf. A144502.
Sequence in context: A004313 A373293 A249981 * A173763 A155649 A184598
KEYWORD
nonn
AUTHOR
STATUS
approved