A255846 a(n) = 2*n^2 + 14.

14, 16, 22, 32, 46, 64, 86, 112, 142, 176, 214, 256, 302, 352, 406, 464, 526, 592, 662, 736, 814, 896, 982, 1072, 1166, 1264, 1366, 1472, 1582, 1696, 1814, 1936, 2062, 2192, 2326, 2464, 2606, 2752, 2902, 3056, 3214, 3376, 3542, 3712, 3886, 4064, 4246, 4432

Offset: 0

Author

Avi Friedlich, Mar 08 2015

Keywords

• nonn
• easy

Comments

This is the case k=7 of the form (n + sqrt(k))^2 + (n - sqrt(k))^2.

Equivalently, numbers m such that 2*m - 28 is a square.

Links

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

Crossrefs

Cf. A117619.

Subsequence of A047235 and A047451.

Cf. similar sequences listed in A255843.

Programs

Magma

[2*n^2+14: n in [0..50]];

Mathematica

Table[2 n^2 + 14, {n, 0, 50}]

PARI

vector(50, n, n--; 2*n^2+14)

Sage

[2*n^2+14 for n in (0..50)]

Formula

G.f.: 2*(7 - 13*x + 8*x^2)/(1 - x)^3.

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

a(n) = 2*A117619(n).

From Amiram Eldar, Mar 28 2023: (Start)

Sum_{n>=0} 1/a(n) = (1 + sqrt(7)*Pi*coth(sqrt(7)*Pi))/28.

Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(7)*Pi*cosech(sqrt(7)*Pi))/28. (End)

E.g.f.: 2*exp(x)*(7 + x + x^2). - Elmo R. Oliveira, Jan 25 2025

Extensions

Edited by Bruno Berselli, Mar 13 2015