A158551 a(n) = 26*n^2 - 1.

25, 103, 233, 415, 649, 935, 1273, 1663, 2105, 2599, 3145, 3743, 4393, 5095, 5849, 6655, 7513, 8423, 9385, 10399, 11465, 12583, 13753, 14975, 16249, 17575, 18953, 20383, 21865, 23399, 24985, 26623, 28313, 30055, 31849, 33695, 35593, 37543, 39545, 41599, 43705

Offset

1,1

Comments

The identity (26*n^2 - 1)^2 - (169*n^2 - 13)*(2*n)^2 = 1 can be written as a(n)^2 - A158550(n)*A005843(n)^2 = 1.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

G.f.: x*(-25 - 28*x + x^2)/(x-1)^3.

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

From Amiram Eldar, Mar 07 2023: (Start)

Sum_{n>=1} 1/a(n) = (1 - cot(Pi/sqrt(26))*Pi/sqrt(26))/2.

Sum_{n>=1} (-1)^(n+1)/a(n) = (cosec(Pi/sqrt(26))*Pi/sqrt(26) - 1)/2. (End)

Mathematica

LinearRecurrence[{3, -3, 1}, {25, 103, 233}, 40] (* Vincenzo Librandi, Feb 14 2012 *)

Prog

(Magma) I:=[25, 103, 233]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]]; // Vincenzo Librandi, Feb 14 2012
(PARI) for(n=1, 40, print1(26*n^2-1", ")); \\ Vincenzo Librandi, Feb 14 2012

Crossrefs

Cf. A005843, A158550.

Sequence in context: A042220 A114254 A042222 * A044276 A044657 A160437

Adjacent sequences: A158548 A158549 A158550 * A158552 A158553 A158554

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 21 2009

Extensions

Comment rewritten by R. J. Mathar, Oct 16 2009

Status

approved