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A051870
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18-gonal (or octadecagonal) numbers: n(8n-7).
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17
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 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 (info(AT)polprimos.com), Apr 26 2008
This sequence does not contain any triangular numbers other than 0 and 1. See A188892. - T. D. Noe, Apr 13 2011
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REFERENCES
| A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, p. 189.
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LINKS
| O. E. Pol, Determinacion geometrica de los numeros primos y perfectos.
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| 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 a(0)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 06 2010]
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EXAMPLE
| a(2)=16*2+1-15=18; a(3)=16*3+18-15=51 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 06 2010]
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MAPLE
| 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
| s=0; lst={s}; Do[s+=n++ +1; AppendTo[lst, s], {n, 0, 6!, 16}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 16 2008]
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PROG
| (PARI) a(n)=n*(8*n-7) \\ Charles R Greathouse IV, Jul 19 2011
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CROSSREFS
| Cf. A014634, A014635, A033585, A033586, A033587, A035008, A069129, A085250, A129271, A129272, A129273, A129274, A129275, A129276, A129277, A129278.
Cf. n-gonal numbers: A000217, A000290, A000326, A000566, A000567, A001106, A001107, A051682, A051624, A051865-A051876.
Sequence in context: A074173 A092068 A093520 * A175815 A069130 A124711
Adjacent sequences: A051867 A051868 A051869 * A051871 A051872 A051873
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Dec 15 1999
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