A241029 Sum of n-th powers of divisors of 22.
4, 36, 610, 11988, 248914, 5314716, 115151530, 2513845188, 55090232674, 1209627165996, 26585860217050, 584603613083988, 12858141059430034, 282844580595234876, 6222201023261420170, 136884245263581500388, 3011407446068928780994
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (36,-343,792,-484).
Crossrefs
Cf. sum of n-th powers of divisors of even k: A000051 (k=2), A001576 (k=4), A034488 (k=6), A034496 (k=8), A034517 (k=10), A034660 (k=12), A141013 (k=14), A020514 (k=16), A034661 (k=18), A034662 (k=20), this sequence (k=22), A034664 (k=24), A241030 (k=26), A241031 (k=28), A241032 (k=30), A034665 (k=32), A034666 (k=36), A034667 (k=40), A034668 (k=48), A034669 (k=56), A020516 (k=64), A034671 (k=72), A034672 (k=96), A034673 (k=120), A034674 (k=128), A034675 (k=144).
Programs
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Magma
[DivisorSigma(n, 22): n in [0..20]];
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Mathematica
Total[#^Range[0, 20]&/@Divisors[22]] Table[(1 + 2^n) (1 + 11^n), {n, 0, 20}] (* Bruno Berselli, Apr 17 2014 *) LinearRecurrence[{36,-343,792,-484},{4,36,610,11988},30] (* Harvey P. Dale, May 21 2014 *) -
Maxima
makelist((1+2^n)*(1+11^n), n, 0, 20); /* Bruno Berselli, Apr 17 2014 */
Formula
G.f.: 2*(2 - 54*x + 343*x^2 - 396*x^3)/((1 - x)*(1 - 2*x)*(1 - 11*x)*(1 - 22*x)). [Bruno Berselli, Apr 17 2014]
a(n) = (1 + 2^n)*(1 + 11^n). [Bruno Berselli, Apr 17 2014]
Comments