A154600 a(n) = 2*n^2 + 22*n + 9.

33, 61, 93, 129, 169, 213, 261, 313, 369, 429, 493, 561, 633, 709, 789, 873, 961, 1053, 1149, 1249, 1353, 1461, 1573, 1689, 1809, 1933, 2061, 2193, 2329, 2469, 2613, 2761, 2913, 3069, 3229, 3393, 3561, 3733, 3909, 4089, 4273, 4461, 4653, 4849, 5049, 5253

Offset: 1

Author

Vincenzo Librandi, Jan 12 2009

Keywords

• nonn
• easy

Comments

Eleventh diagonal of A144562.

2*a(n) + 103 is a square.

Links

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

Crossrefs

Cf. A144562.

Programs

Magma

I:=[33, 61, 93]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 26 2012

Mathematica

LinearRecurrence[{3, -3, 1}, {33, 61, 93}, 50] (* Vincenzo Librandi, Feb 26 2012 *)
4*Binomial[Range[50]+6,2] - 51 (* G. C. Greubel, May 30 2024 *)

PARI

a(n)=2*n*(n+22)+9 \\ Charles R Greathouse IV, Jan 11 2012

SageMath

[2*n^2+22*n+9 for n in range(1,51)] # G. C. Greubel, May 30 2024

Formula

From Vincenzo Librandi, Feb 26 2012: (Start)

G.f: x*(33 - 38*x + 9*x^2)/(1-x)^3.

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

Sum_{n>=1} 1/a(n) = 257162/3084939 + tan(sqrt(103)*Pi/2)*Pi/(2*sqrt(103)). - Amiram Eldar, Feb 25 2023

E.g.f.: -9 + (9 + 24*x + 2*x^2)*exp(x). - G. C. Greubel, May 30 2024