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A051867
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15-gonal (or pentadecagonal) numbers: n(13n-11)/2.
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3
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0, 1, 15, 42, 82, 135, 201, 280, 372, 477, 595, 726, 870, 1027, 1197, 1380, 1576, 1785, 2007, 2242, 2490, 2751, 3025, 3312, 3612, 3925, 4251, 4590, 4942, 5307, 5685, 6076, 6480, 6897, 7327, 7770, 8226, 8695, 9177, 9672, 10180, 10701
(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(13n-11)/2.
G.f.: x*(1+12*x)/(1-x)^3. - Bruno Berselli, Feb 04 2011
a(n)=13*n+a(n-1)-12 (with a(0)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 06 2010]
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EXAMPLE
| a(1)=13*1+0-12=1; a(2)=13*2+1-12=15; a(3)=13*3+15-12=42 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 06 2010]
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MAPLE
| a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=2*a[n-1]-a[n-2]+13 od: seq(a[n], n=0..41); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 18 2008
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MATHEMATICA
| s=0; lst={s}; Do[s+=n++ +1; AppendTo[lst, s], {n, 0, 6!, 13}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 15 2008]
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CROSSREFS
| Cf. n-gonal numbers: A000217, A000290, A000326, A000566, A000567, A001106, A001107, A051682, A051624, A051865-A051876.
Sequence in context: A070007 A154267 A173351 * A008976 A072119 A069127
Adjacent sequences: A051864 A051865 A051866 * A051868 A051869 A051870
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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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