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A255848 a(n) = 2*n^2 + 18. 1
18, 20, 26, 36, 50, 68, 90, 116, 146, 180, 218, 260, 306, 356, 410, 468, 530, 596, 666, 740, 818, 900, 986, 1076, 1170, 1268, 1370, 1476, 1586, 1700, 1818, 1940, 2066, 2196, 2330, 2468, 2610, 2756, 2906, 3060, 3218, 3380, 3546, 3716, 3890, 4068, 4250, 4436 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
For n>3, the sequence gives the 6th diagonal of triangle in A055096.
Also, this is the case k=9 of the form (n + sqrt(k))^2 + (n - sqrt(k))^2. It is noted that a(n)*n = (n + sqrt(3))^3 + (n - sqrt(3))^3.
Equivalently, numbers m such that 2*m-36 is a square.
LINKS
FORMULA
a(n) = 2*A189834(n).
From Vincenzo Librandi, Mar 08 2015: (Start)
G.f.: 2*(9 - 17*x + 10*x^2)/(1 - x)^3.
a(n) = a(-n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
From Amiram Eldar, Mar 28 2023: (Start)
Sum_{n>=0} 1/a(n) = (1 + 3*Pi*coth(3*Pi))/36.
Sum_{n>=0} (-1)^n/a(n) = (1 + 3*Pi*cosech(3*Pi))/36. (End)
MATHEMATICA
f[n_] := 2 n^2 + 18; Array[f, 50, 0] (* Robert G. Wilson v, Mar 08 2015 *)
CoefficientList[Series[(18 - 34 x + 20 x^2) / (1 - x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Mar 08 2015 *)
LinearRecurrence[{3, -3, 1}, {18, 20, 26}, 50] (* Harvey P. Dale, Aug 20 2021 *)
PROG
(Magma) [2*n^2+18: n in [0..50]]; // Vincenzo Librandi, Mar 08 2015
(PARI) vector(50, n, 2*n^2+18) \\ Derek Orr, Mar 09 2015
(Sage) [2*n^2+18 for n in (0..50)] # Bruno Berselli, Mar 11 2015
CROSSREFS
Cf. A016825 (first differences), A055096, A189834.
Subsequence of A047463.
Cf. similar sequences listed in A255843.
Sequence in context: A054565 A295745 A328934 * A072904 A268284 A367268
KEYWORD
nonn,easy
AUTHOR
Avi Friedlich, Mar 08 2015
EXTENSIONS
Edited by Bruno Berselli, Mar 11 2015
STATUS
approved

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Last modified March 2 16:48 EST 2024. Contains 370497 sequences. (Running on oeis4.)