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A051875
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23-gonal numbers: n(21n-19)/2.
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1
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0, 1, 23, 66, 130, 215, 321, 448, 596, 765, 955, 1166, 1398, 1651, 1925, 2220, 2536, 2873, 3231, 3610, 4010, 4431, 4873, 5336, 5820, 6325, 6851, 7398, 7966, 8555, 9165, 9796, 10448, 11121, 11815, 12530, 13266, 14023, 14801, 15600
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OFFSET
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0,3
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COMMENTS
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Sequence found by reading the line from 0, in the direction 0, 23,... and the parallel line from 1, in the direction 1, 66,..., in the square spiral whose vertices are the generalized 23-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..39.
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(21n-19)/2.
G.f.: x*(1+20*x)/(1-x)^3. - Bruno Berselli, Feb 04 2011
a(n)=21*n+a(n-1)-20 (with a(0)=0) [From Vincenzo Librandi, Aug 06 2010]
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EXAMPLE
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a(1)=21*1+0-20=1; a(2)=21*2+1-20=23; a(3)=21*3+23-20=66 [From Vincenzo Librandi, Aug 06 2010]
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MATHEMATICA
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s=0; lst={s}; Do[s+=n++ +1; AppendTo[lst, s], {n, 0, 7!, 21}]; 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-A051874, this sequence, A051876.
Sequence in context: A107692 A089823 A001346 * A125872 A104945 A141849
Adjacent sequences: A051872 A051873 A051874 * A051876 A051877 A051878
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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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