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A255847
a(n) = 2*n^2 + 16.
3
16, 18, 24, 34, 48, 66, 88, 114, 144, 178, 216, 258, 304, 354, 408, 466, 528, 594, 664, 738, 816, 898, 984, 1074, 1168, 1266, 1368, 1474, 1584, 1698, 1816, 1938, 2064, 2194, 2328, 2466, 2608, 2754, 2904, 3058, 3216, 3378, 3544, 3714, 3888, 4066, 4248, 4434, 4624
OFFSET
0,1
COMMENTS
This is the case k=8 of the form (n + sqrt(k))^2 + (n - sqrt(k))^2.
Equivalently, numbers m such that 2*m - 32 is a square.
FORMULA
G.f.: 2*(8 - 15*x + 9*x^2)/(1 - x)^3.
a(n) = a(-n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
a(n) = 2*A189833(n).
From Amiram Eldar, Mar 28 2023: (Start)
Sum_{n>=0} 1/a(n) = (1 + 2*sqrt(2)*Pi*coth(2*sqrt(2)*Pi))/32.
Sum_{n>=0} (-1)^n/a(n) = (1 + 2*sqrt(2)*Pi*cosech(2*sqrt(2)*Pi))/32. (End)
MATHEMATICA
Table[2 n^2 + 16, {n, 0, 50}]
LinearRecurrence[{3, -3, 1}, {16, 18, 24}, 50] (* Harvey P. Dale, Nov 11 2017 *)
PROG
(PARI) vector(50, n, n--; 2*n^2+16)
(Sage) [2*n^2+16 for n in (0..50)]
(Magma) [2*n^2+16: n in [0..50]];
CROSSREFS
Cf. A189833.
Subsequence of A047467.
Cf. similar sequences listed in A255843.
Sequence in context: A081258 A317423 A337374 * A160778 A057369 A178110
KEYWORD
nonn,easy
AUTHOR
Avi Friedlich, Mar 08 2015
EXTENSIONS
Edited by Bruno Berselli, Mar 13 2015
STATUS
approved