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A051876
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24-gonal numbers: n(11n-10).
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26
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0, 1, 24, 69, 136, 225, 336, 469, 624, 801, 1000, 1221, 1464, 1729, 2016, 2325, 2656, 3009, 3384, 3781, 4200, 4641, 5104, 5589, 6096, 6625, 7176, 7749, 8344, 8961, 9600, 10261, 10944, 11649, 12376, 13125, 13896, 14689, 15504, 16341
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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, 24,... and the parallel line from 1, in the direction 1, 69,..., in the square spiral whose vertices are the generalized 24-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(11n-10).
a(n)=22*n+a(n-1)-21 (with a(0)=0) [From Vincenzo Librandi, Aug 06 2010]
G.f.: x*(1+21*x)/(1-x)^3. [Colin Barker, Jan 10 2012]
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EXAMPLE
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a(1)=22*1+0-21=1; a(2)=22*2+1-21=24; a(3)=22*3+24-21=69 [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!, 22}]; lst [From Vladimir Joseph Stephan Orlovsky, Nov 16 2008]
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PROG
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(PARI) a(n)=n*(11*n-10) \\ Charles R Greathouse IV, Jul 19 2011
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CROSSREFS
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Cf. n-gonal numbers: A000217, A000290, A000326, A000384, A000566, A000567, A001106, A001107, A051682, A051624, A051865-A051875.
Sequence in context: A039331 A043934 A087406 * A069174 A124717 A126378
Adjacent sequences: A051873 A051874 A051875 * A051877 A051878 A051879
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KEYWORD
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nonn,easy,changed
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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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