A100041 a(n) = 2*n^2 + n - 7.

-7, -4, 3, 14, 29, 48, 71, 98, 129, 164, 203, 246, 293, 344, 399, 458, 521, 588, 659, 734, 813, 896, 983, 1074, 1169, 1268, 1371, 1478, 1589, 1704, 1823, 1946, 2073, 2204, 2339, 2478, 2621, 2768, 2919, 3074, 3233, 3396, 3563, 3734, 3909, 4088, 4271, 4458, 4649

Offset: 0

Author

Reinhard Zumkeller, Oct 31 2004

Keywords

• sign
• easy

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).

Crossrefs

Cf. A100036, A100037, A100038, A100039.

Programs

Mathematica

Table[2*n^2 + n - 7, {n, 0, 50}] (* G. C. Greubel, Jul 15 2017 *)
LinearRecurrence[{3,-3,1},{-7,-4,3},50] (* Harvey P. Dale, Mar 25 2021 *)

PARI

a(n)=2*n^2+n-7 \\ Charles R Greathouse IV, Jun 17 2017

Formula

A100035(a(n)) = 5 for n>3.

a(n) = A014105(n) - 7 = A084849(n) - 8 = A100040(n) - 2.

From G. C. Greubel, Jul 15 2017: (Start)

G.f.: (7 - 17 x + 6 x^2)/(-1 + x)^3.

E.g.f.: (2*x^2 + 3*x - 7)*exp(x). (End)