A190576 a(n) = n^2 + 5*n - 5.

1, 9, 19, 31, 45, 61, 79, 99, 121, 145, 171, 199, 229, 261, 295, 331, 369, 409, 451, 495, 541, 589, 639, 691, 745, 801, 859, 919, 981, 1045, 1111, 1179, 1249, 1321, 1395, 1471, 1549, 1629, 1711, 1795, 1881, 1969, 2059, 2151, 2245, 2341

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, May 12 2011

Keywords

• nonn
• easy

Comments

Also a(n) = n^2 + 9*n + 9 if the offset is changed to -1. - R. J. Mathar, May 18 2011

Links

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

Crossrefs

Cf. sequences of the form n^2 + k*n - k : A000290 (k=0), A028387 (k=1), A028872 (k=2), A082111 (k=3), A028884 (k=4).

Programs

Magma

[n^2+5*n-5: n in [1..50]]; // Vincenzo Librandi, Sep 30 2011

Mathematica

k = 5; Table[n^2 + k*n - k, {n, 100}]
LinearRecurrence[{3,-3,1},{1,9,19},50] (* Harvey P. Dale, May 28 2015 *)

PARI

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

Formula

G.f.: x*(-1 - 6*x + 5*x^2) / (x-1)^3. - R. J. Mathar, May 18 2011

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(1)=1, a(2)=9, a(3)=19. - Harvey P. Dale, May 28 2015

Sum_{n>=1} 1/a(n) = 199/495 + Pi*tan(3*sqrt(5)*Pi/2)/(3*sqrt(5)). - Amiram Eldar, Jan 18 2021