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

Author

Bruno Berselli, Mar 01 2013

Keywords

• sign
• easy

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).

Crossrefs

Cf. numbers n such that 2*n + 2*k + 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), A155546.

After a(2), subsequence of A168489.

Programs

Magma

[m: m in [-5..5000] | IsSquare(2*m+11)];

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

Mathematica

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

Maxima

makelist(coeff(taylor(-(5-14*x+5*x^2)/(1-x)^3, x, 0, n), x, n), n, 0, 50);

PARI

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

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

From Elmo R. Oliveira, Nov 17 2024: (Start)

E.g.f.: exp(x)*(2*x^2 - 5) + 5.

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