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A051872
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20-gonal (or icosagonal) numbers: n(9n-8).
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7
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0, 1, 20, 57, 112, 185, 276, 385, 512, 657, 820, 1001, 1200, 1417, 1652, 1905, 2176, 2465, 2772, 3097, 3440, 3801, 4180, 4577, 4992, 5425, 5876, 6345, 6832, 7337, 7860, 8401, 8960, 9537, 10132, 10745, 11376, 12025, 12692, 13377, 14080
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OFFSET
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0,3
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COMMENTS
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This sequence does not contain any squares other than 0 and 1. See A188896. - T. D. Noe, Apr 13 2011
Sequence found by reading the line from 0, in the direction 0, 20,... and the parallel line from 1, in the direction 1, 57,..., in the square spiral whose vertices are the generalized 20-gonal numbers. - Omar E. Pol, Jul 18 2012
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REFERENCES
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A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, p. 189.
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LINKS
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Table of n, a(n) for n=0..40.
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(9n-8).
G.f.: x*(1+17*x)/(1-x)^3. - Bruno Berselli, Feb 04 2011
a(n)=18*n+a(n-1)-17 (with a(0)=0) [From Vincenzo Librandi, Aug 06 2010]
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EXAMPLE
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a(1)=18*1+0-17=1; a(2)=18*2+1-17=20; a(3)=18*3+20-17=57 [From Vincenzo Librandi, Aug 06 2010]
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MAPLE
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A051872 := proc(n) n*(9*n-8) ; end proc: seq(A051872(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, 7!, 18}]; lst [From Vladimir Joseph Stephan Orlovsky, Nov 16 2008]
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CROSSREFS
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Cf. n-gonal numbers: A000217, A000290, A000326, A000384, A000566, A000567, A001106, A001107, A051682, A051624, A051865-A051871, this sequence, A051873-A051876.
Sequence in context: A109806 A216267 A012483 * A104100 A069132 A124713
Adjacent sequences: A051869 A051870 A051871 * A051873 A051874 A051875
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KEYWORD
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nonn
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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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