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A051874
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22-gonal numbers: n(10n-9).
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3
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0, 1, 22, 63, 124, 205, 306, 427, 568, 729, 910, 1111, 1332, 1573, 1834, 2115, 2416, 2737, 3078, 3439, 3820, 4221, 4642, 5083, 5544, 6025, 6526, 7047, 7588, 8149, 8730, 9331, 9952, 10593, 11254, 11935, 12636, 13357, 14098, 14859
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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, 22,... and the parallel line from 1, in the direction 1, 63,..., in the square spiral whose vertices are the generalized 22-gonal numbers. - Omar E. Pol, Jul 18 2012
Also sequence found by reading the segment (0, 1) together with the line from 1, in the direction 1, 22,..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. - Omar E. Pol, Jul 29 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..39.
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(10n-9).
G.f.: x*(1+19*x)/(1-x)^3. - Bruno Berselli, Feb 04 2011
a(n)=2*a(n-1)-a(n-2)+20 with n>1, a(0)=0, a(1)=1. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 18 2008
a(n)=20*n+a(n-1)-19 (with a(0)=0) [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]+20 od: seq(a[n], n=0..39); - 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, 7!, 20}]; lst [From Vladimir Joseph Stephan Orlovsky, Nov 16 2008]
Table[n(10n-9), {n, 0, 40}] (* From Harvey P. Dale, Sep 19 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-A051873, this sequence, A081875, A051876.
Sequence in context: A156797 A216299 A221595 * A140390 A069178 A081929
Adjacent sequences: A051871 A051872 A051873 * A051875 A051876 A051877
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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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