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A139275 a(n) = n*(8*n+1). 18
0, 9, 34, 75, 132, 205, 294, 399, 520, 657, 810, 979, 1164, 1365, 1582, 1815, 2064, 2329, 2610, 2907, 3220, 3549, 3894, 4255, 4632, 5025, 5434, 5859, 6300, 6757, 7230, 7719, 8224, 8745, 9282, 9835, 10404, 10989, 11590, 12207, 12840 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Sequence found by reading the line from 0, in the direction 0, 9,..., in the square spiral whose vertices are the triangular numbers A000217.
LINKS
FORMULA
a(n) = 8*n^2 + n.
Sequences of the form a(n) = 8*n^2+c*n have generating functions x{c+8+(8-c)x} / (1-x)^3 and recurrence a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). The inverse binomial transform is 0, c+8, 16, 0, 0, ... (0 continued). This applies to A139271-A139278, positive or negative c. - R. J. Mathar, May 12 2008
a(n) = 16*n + a(n-1) - 7 with n>0, a(0)=0. - Vincenzo Librandi, Aug 03 2010
a(n) = A000217(5*n) - A000217(3*n). - Bruno Berselli, Sep 21 2016
Sum_{n>=1} 1/a(n) = 8 - (1+sqrt(2))*Pi/2 - 4*log(2) - sqrt(2) * log(1+sqrt(2)) = 0.1887230016056779928... . - Vaclav Kotesovec, Sep 21 2016
From G. C. Greubel, Jul 18 2017: (Start)
G.f.: x*(7*x + 9)/(1-x)^3.
E.g.f.: (8*x^2 + 9*x)*exp(x). (End)
MATHEMATICA
Table[n (8 n + 1), {n, 0, 40}] (* Bruno Berselli, Sep 21 2016 *)
LinearRecurrence[{3, -3, 1}, {0, 9, 34}, 50] (* Harvey P. Dale, Apr 21 2020 *)
PROG
(PARI) a(n) = n*(8*n+1); \\ Altug Alkan, Sep 21 2016
CROSSREFS
Sequence in context: A044467 A020163 A262959 * A236370 A273744 A133547
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Apr 26 2008
STATUS
approved

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Last modified May 25 03:39 EDT 2024. Contains 372782 sequences. (Running on oeis4.)