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

0,2

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).

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)

Mathematica

13*Range[0, 40]^2 (* or *) LinearRecurrence[{3, -3, 1}, {0, 13, 52}, 40] (* Harvey P. Dale, Feb 18 2015 *)

Prog

(PARI) a(n)=13*n^2 \\ Charles R Greathouse IV, Oct 07 2015
(Magma) [13*n^2: n in [0..50]]; // G. C. Greubel, Sep 01 2018

Crossrefs

Cf. A000290, A135453.

Sequence in context: A002792 A183941 A022673 * A213837 A047903 A197790

Adjacent sequences: A152739 A152740 A152741 * A152743 A152744 A152745

Keyword

easy,nonn

Author

Omar E. Pol, Dec 12 2008

Status

approved