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A051868
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16-gonal (or hexadecagonal) numbers: n*(7*n-6).
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5
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0, 1, 16, 45, 88, 145, 216, 301, 400, 513, 640, 781, 936, 1105, 1288, 1485, 1696, 1921, 2160, 2413, 2680, 2961, 3256, 3565, 3888, 4225, 4576, 4941, 5320, 5713, 6120, 6541, 6976, 7425, 7888, 8365, 8856, 9361, 9880, 10413, 10960, 11521
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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, 16,... and the parallel line from 1, in the direction 1, 45,..., in the square spiral whose vertices are the generalized 16-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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Table of n, a(n) for n=0..41.
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*(7*n-6).
G.f.: x*(1+13*x)/(1-x)^3. - Bruno Berselli, Feb 04 2011
a(0)=0, a(1)=1, a(2)=16, a(n)=3*a(n-1)-3*a(n-2)+a(n-3) [From Harvey P. Dale, May 07 2011]
a(n)=14*n+a(n-1)-13 (with a(0)=0) [From Vincenzo Librandi, Aug 06 2010]
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EXAMPLE
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a(1)=14*1+0-13=1; a(2)=14*2+1-13=16; a(3)=14*3+16-13=45 [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]+14 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!, 14}]; lst [From Vladimir Joseph Stephan Orlovsky, Nov 16 2008]
Table[n(7n-6), {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 1, 16}, 51] (* From Harvey P. Dale, May 07 2011 *)
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CROSSREFS
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Cf. n-gonal numbers: A000217, A000290, A000326, A000384, A000566, A000567, A001106, A001107, A051682, A051624, A051865-A051867, this sequence, A051869-A051876.
Sequence in context: A204032 A192143 A221593 * A209993 A223029 A069128
Adjacent sequences: A051865 A051866 A051867 * A051869 A051870 A051871
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KEYWORD
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nonn
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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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