A169642 a(n) = A005408(n) * A022998(n).

0, 3, 20, 21, 72, 55, 156, 105, 272, 171, 420, 253, 600, 351, 812, 465, 1056, 595, 1332, 741, 1640, 903, 1980, 1081, 2352, 1275, 2756, 1485, 3192, 1711, 3660, 1953, 4160, 2211, 4692, 2485, 5256, 2775, 5852, 3081, 6480, 3403, 7140, 3741, 7832, 4095, 8556

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).

Formula

From R. J. Mathar, Oct 09 2010: (Start)

a(n)= +3*a(n-2) -3*a(n-4) +a(n-6).

G.f.: -x*(3+20*x+12*x^2+12*x^3+x^4)/ ( (x-1)^3*(1+x)^3 ). (End)

From Colin Barker, Dec 29 2016: (Start)

a(n) = 4*n^2 + 2*n for n>0 and even.

a(n) = 2*n^2 + n for n odd. (End)

Sum_{n>=1} 1/a(n) = 1 + Pi/8 - 5*log(2)/4. - Amiram Eldar, Aug 12 2022

Mathematica

LinearRecurrence[{0, 3, 0, -3 , 0, 1}, {0 , 3, 20, 21, 72, 55}, 47] (* Georg Fischer, Feb 22 2019 *)

Prog

(PARI) concat(0, Vec(-x*(3+20*x+12*x^2+12*x^3+x^4)/ ((x-1)^3*(1+x)^3) + O(x^50))) \\ Colin Barker, Dec 29 2016

Crossrefs

Cf. A005408, A022998.

Sequence in context: A081849 A333667 A375618 * A222482 A022129 A308721

Adjacent sequences: A169639 A169640 A169641 * A169643 A169644 A169645

Keyword

nonn,easy

Author

Paul Curtz, Apr 04 2010

Extensions

Edited by N. J. A. Sloane, Apr 05 2010

More terms from R. J. Mathar, Oct 09 2010

Status

approved