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A033568 Second pentagonal numbers with odd index: a(n) = (2*n-1)*(3*n-1). 15
1, 2, 15, 40, 77, 126, 187, 260, 345, 442, 551, 672, 805, 950, 1107, 1276, 1457, 1650, 1855, 2072, 2301, 2542, 2795, 3060, 3337, 3626, 3927, 4240, 4565, 4902, 5251, 5612, 5985, 6370, 6767, 7176, 7597, 8030, 8475, 8932, 9401, 9882, 10375, 10880, 11397, 11926 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Sequence found by reading the segment (1, 2) together with the line (one of the diagonal axes) from 2, in the direction 2, 15, ..., in the square spiral whose vertices are the generalized pentagonal numbers A001318. - Omar E. Pol, Sep 08 2011
LINKS
FORMULA
G.f.: (1-x+12*x^2)/(1-x)^3.
a(n) = a(n-1) + 12*n - 11 (with a(0)=1). - Vincenzo Librandi, Nov 17 2010
a(n) = 6*n^2 - 5*n + 1 = A051866(n) + 1. - Omar E. Pol, Jul 18 2012
E.g.f.: (1 + x + 6*x^2)*exp(x). - G. C. Greubel, Oct 12 2019
From Amiram Eldar, Feb 18 2022: (Start)
Sum_{n>=0} 1/a(n) = 1 + Pi/(2*sqrt(3)) + 2*log(2) - 3*log(3)/2.
Sum_{n>=0} (-1)^n/a(n) = 1 + (1/sqrt(3) - 1/2)*Pi - log(2). (End)
MAPLE
seq((2*n-1)*(3*n-1), n=0..50); # G. C. Greubel, Oct 12 2019
MATHEMATICA
Table[(2*n-1)*(3*n-1), {n, 0, 50}] (* Vladimir Joseph Stephan Orlovsky, Apr 28 2010 *)
LinearRecurrence[{3, -3, 1}, {1, 2, 15}, 50] (* Ray Chandler, Dec 08 2011 *)
PROG
(PARI) a(n)=(2*n-1)*(3*n-1) \\ Charles R Greathouse IV, Sep 24 2015
(Magma) [(2*n-1)*(3*n-1): n in [0..50]]; // G. C. Greubel, Oct 12 2019
(Sage) [(2*n-1)*(3*n-1) for n in range(50)] # G. C. Greubel, Oct 12 2019
(GAP) List([0..50], n-> (2*n-1)*(3*n-1)); # G. C. Greubel, Oct 12 2019
CROSSREFS
Sequence in context: A180223 A070009 A070170 * A200156 A249997 A032016
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Ray Chandler, Dec 08 2011
STATUS
approved

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)