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
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).
Programs
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Mathematica
LinearRecurrence[{0, 3, 0, -3 , 0, 1}, {0 , 3, 20, 21, 72, 55}, 47] (* Georg Fischer, Feb 22 2019 *) -
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
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
Extensions
Edited by N. J. A. Sloane, Apr 05 2010
More terms from R. J. Mathar, Oct 09 2010