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A051682
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11-gonal (or hendecagonal) numbers: n(9n-7)/2.
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67
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0, 1, 11, 30, 58, 95, 141, 196, 260, 333, 415, 506, 606, 715, 833, 960, 1096, 1241, 1395, 1558, 1730, 1911, 2101, 2300, 2508, 2725, 2951, 3186, 3430, 3683, 3945, 4216, 4496, 4785, 5083, 5390, 5706, 6031, 6365, 6708, 7060, 7421, 7791, 8170
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OFFSET
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0,3
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COMMENTS
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Write 0,1,2,3,4,... in a triangular spiral, then a(n) is the sequence found by reading the line from 0 in the direction 0,1,... - Floor van Lamoen (fvlamoen(AT)hotmail.com), Jul 21 2001. The spiral begins:
......15
....16..14
..17..3...13
18..4...2...12
..5...0...1...11
6...7...8...9...10
(1), (4+7), (7+10+13), (10+13+16+19), ... - Jon Perry, Sep 10 2004
This sequence does not contain any triangular numbers other than 0 and 1. See A188892. - T. D. Noe, Apr 13 2011
Sequence found by reading the line from 0, in the direction 0, 11,... and the parallel line from 1, in the direction 1, 30,..., in the square spiral whose vertices are the generalized 11-gonal numbers A195160. - 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, pp. 189, 194-196.
Murray R. Spiegel, Calculus of Finite Differences and Difference Equations, "Schaum's Outline Series", McGraw-Hill, 1971, pps. 10-20, 79-94.
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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*(9*n-7)/2.
G.f.: x*(1+8*x)/(1-x)^3.
Row sums of triangle A131432 - Gary W. Adamson, Jul 10 2007
a(n)=9*n+a(n-1)-8 (with a(0)=0) [From Vincenzo Librandi, Aug 06 2010]
a(0)=0, a(1)=1, a(2)=11, a(n)=3*a(n-1)-3*a(n-2)+a(n-3) [From Harvey P. Dale, May 07 2012]
a(n) = A218470(9n). - Philippe Deléham, Mar 27 2013
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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]+9 od: seq(a[n], n=0..43); - 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!, 9}]; lst [From Vladimir Joseph Stephan Orlovsky, Nov 15 2008]
Table[n (9n-7)/2, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 1, 11}, 51] (* From Harvey P. Dale, May 07 2012 *)
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PROG
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(PARI) a(n)=(9*n-7)*n/2 \\ Charles R Greathouse IV, Jun 16 2011
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CROSSREFS
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First differences of A007586.
Cf. A093644 ((9, 1) Pascal, column m=2). Partial sums of A017173.
Cf. A004188.
Cf. A131432.
Cf. n-gonal numbers: A000217, A000290, A000326, A000384, A000566, A000567, A001106, A001107, this sequence, A051624, A051865-A051876.
Sequence in context: A146751 A162734 A163060 * A109943 A137411 A002755
Adjacent sequences: A051679 A051680 A051681 * A051683 A051684 A051685
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KEYWORD
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easy,nonn,changed
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AUTHOR
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Barry E. Williams
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EXTENSIONS
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More terms from James A. Sellers, Dec 08 1999
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STATUS
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approved
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