A152742 13 times the squares: a(n) = 13*n^2.
0, 13, 52, 117, 208, 325, 468, 637, 832, 1053, 1300, 1573, 1872, 2197, 2548, 2925, 3328, 3757, 4212, 4693, 5200, 5733, 6292, 6877, 7488, 8125, 8788, 9477, 10192, 10933, 11700, 12493, 13312, 14157, 15028, 15925, 16848, 17797, 18772
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..5000
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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Magma
[13*n^2: n in [0..50]]; // G. C. Greubel, Sep 01 2018
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Mathematica
13*Range[0,40]^2 (* or *) LinearRecurrence[{3,-3,1},{0,13,52},40] (* Harvey P. Dale, Feb 18 2015 *) -
PARI
a(n)=13*n^2 \\ Charles R Greathouse IV, Oct 07 2015
Formula
a(n) = 13*A000290(n).
a(n) = a(n-1) +26*n -13 (with a(0)=0). - Vincenzo Librandi, Nov 26 2010
a(0)=0, a(1)=13, a(2)=52, a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - Harvey P. Dale, Feb 18 2015
From G. C. Greubel, Sep 01 2018:(Start)
G.f.: 13*x*(1+x)/(1-x)^3.
E.g.f.: 13*(1+x)*exp(x). (End)
From Amiram Eldar, Feb 03 2021: (Start)
Sum_{n>=1} 1/a(n) = Pi^2/78.
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/156.
Product_{n>=1} (1 + 1/a(n)) = sqrt(13)*sinh(Pi/sqrt(13))/Pi.
Product_{n>=1} (1 - 1/a(n)) = sqrt(13)*sin(Pi/sqrt(13))/Pi. (End)