A082113 a(n) = n^4 + 5*n^2 + 1.

1, 7, 37, 127, 337, 751, 1477, 2647, 4417, 6967, 10501, 15247, 21457, 29407, 39397, 51751, 66817, 84967, 106597, 132127, 162001, 196687, 236677, 282487, 334657, 393751, 460357, 535087, 618577, 711487, 814501, 928327, 1053697, 1191367

Offset: 0

Author

Paul Barry, Apr 04 2003

Keywords

• easy
• nonn

Comments

Main diagonal of number array A082110.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A082044, A082047, A082106.

Programs

Magma

[n^4+5*n^2+1: n in [0..40]]; // G. C. Greubel, Dec 22 2022

Mathematica

Table[n^4+5n^2+1,{n,0,40}] (* or *) LinearRecurrence[{5,-10,10,-5,1},{1,7,37,127,337},40] (* Harvey P. Dale, May 16 2019 *)

SageMath

[n^4+5*n^2+1 for n in range(41)] # G. C. Greubel, Dec 22 2022

Formula

a(n) = n^4 + 5*n^2 + 1.

G.f.: (1+2*x+12*x^2+2*x^3+7*x^4) / (1-x)^5. - R. J. Mathar, Dec 03 2014

E.g.f.: (1 + 6*x + 12*x^2 + 6*x^3 + x^4)*exp(x). - G. C. Greubel, Dec 22 2022