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A051865
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13-gonal (or tridecagonal) numbers: n(11n-9)/2.
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42
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0, 1, 13, 36, 70, 115, 171, 238, 316, 405, 505, 616, 738, 871, 1015, 1170, 1336, 1513, 1701, 1900, 2110, 2331, 2563, 2806, 3060, 3325, 3601, 3888, 4186, 4495, 4815, 5146, 5488, 5841, 6205, 6580, 6966, 7363, 7771, 8190, 8620, 9061, 9513
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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, 13,... and the parallel line from 1, in the direction 1, 36,..., in the square spiral whose vertices are the generalized 13-gonal numbers A195313. - 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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T. D. Noe, 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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a(n)=n(11n-9)/2.
G.f.: x*(1+10*x)/(1-x)^3. - Bruno Berselli, Feb 04 2011
a(n)=11*n+a(n-1)-10 (with a(0)=0) [From Vincenzo Librandi, Aug 06 2010]
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EXAMPLE
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a(1)=11*1+0-10=1; a(2)=11*2+1-10=13; a(3)=11*3+13-10=36 [From Vincenzo Librandi, Aug 06 2010]
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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]+11 od: seq(a[n], n=0..42); - 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!, 11}]; lst [From Vladimir Joseph Stephan Orlovsky, Nov 15 2008]
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PROG
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(PARI) a(n)=(11*n^2-9*n)/2 \\ Charles R Greathouse IV, May 27 2011
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CROSSREFS
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Cf. n-gonal numbers: A000217, A000290, A000326, A000384, A000566, A000567, A001106, A001107, A051682, A051624, this sequence, A051866-A051876.
Sequence in context: A034119 A054285 A101103 * A081928 A034129 A225131
Adjacent sequences: A051862 A051863 A051864 * A051866 A051867 A051868
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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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