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A051872
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20-gonal (or icosagonal) numbers: n(9n-8).
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5
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| This sequence does not contain any squares other than 0 and 1. See A188896. - 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
| Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| 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 (vincenzo.librandi(AT)tin.it), Aug 06 2010]
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EXAMPLE
| a(1)=18*1+0-17=1; a(2)=18*2+1-17=20; a(3)=18*3+20-17=57 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 06 2010]
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MAPLE
| 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
| s=0; lst={s}; Do[s+=n++ +1; AppendTo[lst, s], {n, 0, 7!, 18}]; 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: A044503 A109806 A012483 * A104100 A069132 A124713
Adjacent sequences: A051869 A051870 A051871 * A051873 A051874 A051875
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Dec 15 1999
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