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A051867
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15-gonal (or pentadecagonal) numbers: n(13n-11)/2.
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6
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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
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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, 15,... and the parallel line from 1, in the direction 1, 42,..., in the square spiral whose vertices are the generalized 15-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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Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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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) - Vincenzo Librandi, Aug 06 2010
a(0)=0, a(1)=1, a(2)=15, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, Feb 29 2012
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MAPLE
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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
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s=0; lst={s}; Do[s+=n++ +1; AppendTo[lst, s], {n, 0, 6!, 13}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 15 2008 *)
Table[n (13n-11)/2, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 1, 15}, 50] (* Harvey P. Dale, Feb 29 2012 *)
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CROSSREFS
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Cf. n-gonal numbers: A000217, A000290, A000326, A000384, A000566, A000567, A001106, A001107, A051682, A051624, A051865, A051866, this sequence, A051868-A051876.
Sequence in context: A070007 A154267 A173351 * A008976 A072119 A069127
Adjacent sequences: A051864 A051865 A051866 * A051868 A051869 A051870
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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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