A154591 a(n) = 2*n^2 + 18*n + 7.

27, 51, 79, 111, 147, 187, 231, 279, 331, 387, 447, 511, 579, 651, 727, 807, 891, 979, 1071, 1167, 1267, 1371, 1479, 1591, 1707, 1827, 1951, 2079, 2211, 2347, 2487, 2631, 2779, 2931, 3087, 3247, 3411, 3579, 3751, 3927, 4107, 4291, 4479, 4671, 4867, 5067, 5271

Offset

1,1

Comments

Ninth diagonal of A144562.

2*a(n) + 67 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).

Formula

G.f.: (9*x^2-6*x-7)/(x-1)^3. - Bruno Berselli, Dec 07 2011

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Feb 22 2012

Sum_{n>=1} 1/a(n) = 1621/20097 + tan(sqrt(67)*Pi/2)*Pi/(2*sqrt(67)). - Amiram Eldar, Feb 25 2023

E.g.f.: (7 + 20*x + 2*x^2)*exp(x). - G. C. Greubel, May 27 2024

Mathematica

LinearRecurrence[{3, -3, 1}, {27, 51, 79}, 50] (* Vincenzo Librandi, Feb 22 2012 *)

Prog

(Magma) I:=[27, 51, 79]; [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 22 2012
(PARI) for(n=1, 40, print1(2*n^2 + 18*n + 7", ")); \\ Vincenzo Librandi, Feb 22 2012
(SageMath) [2*n^2+18*n+7 for n in range(1, 51)] #  G. C. Greubel, May 27 2024

Crossrefs

Cf. A067076, A144562, A153238.

Sequence in context: A034595 A330279 A102708 * A217235 A265683 A044079

Adjacent sequences: A154588 A154589 A154590 * A154592 A154593 A154594

Keyword

nonn,easy

Author

Vincenzo Librandi, Jan 12 2009

Status

approved