A172193 a(n) = 5*n^2 + 31*n + 1.

1, 37, 83, 139, 205, 281, 367, 463, 569, 685, 811, 947, 1093, 1249, 1415, 1591, 1777, 1973, 2179, 2395, 2621, 2857, 3103, 3359, 3625, 3901, 4187, 4483, 4789, 5105, 5431, 5767, 6113, 6469, 6835, 7211, 7597, 7993, 8399, 8815, 9241, 9677, 10123, 10579

Offset: 0

Author

Vincenzo Librandi, Jan 29 2010

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A172043 (5*n^2-n+1).

Programs

Magma

[ 5*n^2+31*n+1: n in [0..50] ];

Mathematica

CoefficientList[Series[(1 +34x -25x^2)/(1-x)^3, {x, 0, 60}], x] (* Vincenzo Librandi, Apr 07 2013 *)
LinearRecurrence[{3,-3,1},{1,37,83},50] (* Harvey P. Dale, May 16 2025 *)

PARI

a(n)=5*n^2+31*n+1 \\ Charles R Greathouse IV, Jun 17 2017

SageMath

[((10*n+31)^2 -941)/20 for n in (0..50)] # G. C. Greubel, Apr 28 2022

Formula

G.f.: (1+34*x-25*x^2)/(1-x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Apr 07 2013

E.g.f.: (1 + 36*x + 5*x^2)*exp(x). - G. C. Greubel, Apr 28 2022

Extensions

Replaced definition with formula. - N. J. A. Sloane, Mar 03 2010