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A051870
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18-gonal (or octadecagonal) numbers: n(8n-7).
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20
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0, 1, 18, 51, 100, 165, 246, 343, 456, 585, 730, 891, 1068, 1261, 1470, 1695, 1936, 2193, 2466, 2755, 3060, 3381, 3718, 4071, 4440, 4825, 5226, 5643, 6076, 6525, 6990, 7471, 7968, 8481, 9010, 9555, 10116, 10693, 11286, 11895, 12520
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OFFSET
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0,3
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COMMENTS
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Also, sequence found by reading the segment (0, 1) together with the line from 1, in the direction 1, 18,..., in the square spiral whose vertices are the triangular numbers A000217. - Omar E. Pol, Apr 26 2008.
This sequence does not contain any triangular numbers other than 0 and 1. See A188892. - T. D. Noe, Apr 13 2011.
Also sequence found by reading the line from 0, in the direction 0, 18,... and the parallel line from 1, in the direction 1, 51,..., in the square spiral whose vertices are the generalized 18-gonal numbers. - Omar E. Pol, Jul 18 2012.
Partial sums of 16n + 1 (with offset 0), compare A005570. - Jeremy Gardiner, Aug 04 2012.
All x values for Diophantine equation 32*x+49 = y^2 are given by this sequence and A139278. [Bruno Berselli, Nov 11 2014]
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REFERENCES
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A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, p. 189.
E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 6.
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LINKS
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Jeremy Gardiner, Table of n, a(n) for n = 0..999
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.
Wikipedia, Polygonal number.
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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a(n) = n(8n-7).
G.f.: x*(1+15*x)/(1-x)^3. - Bruno Berselli, Feb 04 2011
a(n) = 16*n+a(n-1)-15, with n>0, a(0)=0. [Vincenzo Librandi, Aug 06 2010]
a(16*a(n)+121*n+1) = a(16*a(n)+121*n) + a(16*n+1). - Vladimir Shevelev, Jan 24 2014
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MAPLE
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A051870 := proc(n) n*(8*n-7) ; end proc: seq(A051870(n), n=0..30) ; # R. J. Mathar, Feb 05 2011
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MATHEMATICA
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s=0; lst={s}; Do[s+=n++ +1; AppendTo[lst, s], {n, 0, 6!, 16}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 16 2008 *)
Table[n (8 n - 7), {n, 0, 40}] (* Bruno Berselli, Nov 11 2014 *)
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PROG
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(PARI) a(n)=n*(8*n-7) \\ Charles R Greathouse IV, Jul 19 2011
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CROSSREFS
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Cf. A014634, A014635, A033585, A033586, A033587, A035008, A069129, A085250, A129271 - A129278, A139278.
Cf. n-gonal numbers: A000217, A000290, A000326, A000384, A000566, A000567, A001106, A001107, A051682, A051624, A051865-A051869, this sequence, A051871-A051876.
Sequence in context: A074173 A092068 A093520 * A175815 A069130 A124711
Adjacent sequences: A051867 A051868 A051869 * A051871 A051872 A051873
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Dec 15 1999
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STATUS
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approved
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