A222182 Numbers m such that 2*m+11 is a square.

-5, -1, 7, 19, 35, 55, 79, 107, 139, 175, 215, 259, 307, 359, 415, 475, 539, 607, 679, 755, 835, 919, 1007, 1099, 1195, 1295, 1399, 1507, 1619, 1735, 1855, 1979, 2107, 2239, 2375, 2515, 2659, 2807, 2959, 3115, 3275, 3439, 3607, 3779, 3955, 4135, 4319, 4507, 4699

Offset

1,1

Comments

Except the first term, main diagonal of A155546. - Vincenzo Librandi, Mar 04 2013

Links

Bruno Berselli, Table of n, a(n) for n = 1..1000

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

Formula

G.f.: -x*(5-14*x+5*x^2)/(1-x)^3.

a(n) = a(-n+1) = 2*n^2-2*n-5.

a(n) = A046092(n-1)-5.

Sum_{n>=1} 1/a(n) = Pi*tan(sqrt(11)*Pi/2)/(2*sqrt(11)). - Amiram Eldar, Dec 23 2022

Mathematica

Table[2 n^2 - 2 n - 5, {n, 50}]

Prog

(Magma) [m: m in [-5..5000] | IsSquare(2*m+11)];
(Maxima) makelist(coeff(taylor(-(5-14*x+5*x^2)/(1-x)^3, x, 0, n), x, n), n, 0, 50);
(Magma) I:=[-5, -1, 7]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]]; // Vincenzo Librandi, Mar 04 2013
(PARI) a(n)=2*n^2-2*n-5 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. numbers n such that 2n+2k+1 is a square: A046092 (k=0), A142463 (k=1), A090288 (k=2), A059993 (k=3), A139570 (k=4), this sequence (k=5), A181510 (k=6).

Cf. A005408 (square roots of 2*a(n)+11).

After a(2), subsequence of A168489.

Cf. A155546.

Sequence in context: A193860 A211849 A363419 * A126155 A021197 A286872

Adjacent sequences: A222179 A222180 A222181 * A222183 A222184 A222185

Keyword

sign,easy

Author

Bruno Berselli, Mar 01 2013

Status

approved