A145980 a(n) = 29 + 73*n + 37*n^2.

29, 139, 323, 581, 913, 1319, 1799, 2353, 2981, 3683, 4459, 5309, 6233, 7231, 8303, 9449, 10669, 11963, 13331, 14773, 16289, 17879, 19543, 21281, 23093, 24979, 26939, 28973, 31081, 33263, 35519, 37849, 40253, 42731, 45283, 47909, 50609, 53383, 56231, 59153, 62149, 65219, 68363

Offset: 0

Author

Paul Curtz, Oct 26 2008

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Programs

Magma

[29+73*n+37*n^2: n in [0..40]]; // Vincenzo Librandi, Aug 07 2011

Mathematica

LinearRecurrence[{3, -3, 1}, {29, 139, 323}, 50] (* G. C. Greubel, Jan 29 2016 *)

PARI

a(n)=29+73*n+37*n^2 \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = A061037(4n+2)+A061037(4n+3)+A061037(4n+4)+A061037(4n+5).

From R. J. Mathar, Oct 31 2008 (Start)

a(n) = 3*a(n-1)-3*a(n-2)+a(n-3).

G.f.: (29+52*x-7*x^2)/(1-x)^3. (End)

E.g.f.: (37*x^2 + 110*x + 29)*exp(x). - G. C. Greubel, Jan 29 2016

Extensions

Indices in definition edited, extended beyond a(13) by R. J. Mathar, Oct 31 2008