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A051875
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23-gonal numbers: n(21n-19)/2.
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0
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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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
| Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| 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 (vincenzo.librandi(AT)tin.it), Aug 06 2010]
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EXAMPLE
| a(1)=21*1+0-20=1; a(2)=21*2+1-20=23; a(3)=21*3+23-20=66 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 06 2010]
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MATHEMATICA
| s=0; lst={s}; Do[s+=n++ +1; AppendTo[lst, s], {n, 0, 7!, 21}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 16 2008]
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CROSSREFS
| Cf. n-gonal numbers: A000217, A000290, A000326, A000566, A000567, A001106, A001107, A051682, A051624, A051865-A051876.
Sequence in context: A107692 A089823 A001346 * A125872 A104945 A141849
Adjacent sequences: A051872 A051873 A051874 * A051876 A051877 A051878
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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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