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A014641
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Odd octagonal numbers: (2n+1)(6n+1).
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12
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1, 21, 65, 133, 225, 341, 481, 645, 833, 1045, 1281, 1541, 1825, 2133, 2465, 2821, 3201, 3605, 4033, 4485, 4961, 5461, 5985, 6533, 7105, 7701, 8321, 8965, 9633, 10325, 11041, 11781, 12545, 13333, 14145, 14981, 15841, 16725, 17633, 18565, 19521, 20501, 21505
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OFFSET
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0,2
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COMMENTS
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Sequence found by reading the line from 1, in the direction 1, 21, ..., in the square spiral whose vertices are the generalized octagonal numbers A001082. - Omar E. Pol, Jul 18 2012
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LINKS
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Muniru A Asiru, Table of n, a(n) for n = 0..5000
Richard P. Brent, Generalising Tuenter's binomial sums, arXiv:1407.3533 [math.CO], 2014.
Richard P. Brent, Generalising Tuenter's binomial sums, Journal of Integer Sequences, 18 (2015), Article 15.3.2.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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a(n) = a(n-1) + 24*n - 4, with n > 0, a(0)=1. - Vincenzo Librandi, Dec 28 2010
G.f.: (1 + 18*x + 5*x^2)/(1 - 3*x + 3*x^2 - x^3). - Colin Barker, Jan 06 2012
a(n) = A289873(6*n+2). - Hugo Pfoertner, Jul 15 2017
From Peter Bala, Jan 22 2018: (Start)
This is the polynomial Qbar(2,n) in Brent. See A160485 for the triangle of coefficients (with signs) of the Qbar polynomials.
a(n) = (1/4^n) * Sum_{k = 0..n} (2*k + 1)^4*binomial(2*n + 1, n - k).
a(n-1) = (2/4^n) * binomial(2*n,n) * ( 1 + 3^4*(n - 1)/(n + 1) + 5^4*(n - 1)*(n - 2)/((n + 1)*(n + 2)) + 7^4*(n - 1)*(n - 2)*(n - 3)/((n + 1)*(n + 2)*(n + 3)) + ... ). (End)
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MAPLE
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A014641:=n->(2*n+1)*(6*n+1); seq(A014641(n), n=0..50); # Wesley Ivan Hurt, Jun 08 2014
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MATHEMATICA
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Table[(2n + 1)(6n + 1), {n, 0, 49}] (* Harvey P. Dale, Mar 24 2011 *)
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PROG
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(MAGMA) [ (2*n+1)*(6*n+1) : n in [0..50] ]; // Wesley Ivan Hurt, Jun 08 2014
(PARI) a(n)=(2*n+1)*(6*n+1) \\ Charles R Greathouse IV, Jun 17 2017
(GAP) List([0..50], n->(2*n+1)*(6*n+1)); # Muniru A Asiru, Feb 05 2019
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CROSSREFS
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Cf. A000567, A014642, A014793, A014794, A243201, A289873.
Cf. A160485, A245244.
Sequence in context: A041864 A041866 A020211 * A259677 A089115 A259244
Adjacent sequences: A014638 A014639 A014640 * A014642 A014643 A014644
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KEYWORD
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nonn,easy
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AUTHOR
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Mohammad K. Azarian, Dec 11 1999
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EXTENSIONS
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More terms from Patrick De Geest
Better description from N. J. A. Sloane
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STATUS
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approved
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