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A051682
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11-gonal (or hendecagonal) numbers: n(9n-7)/2.
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60
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 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 (perry(AT)globalnet.co.uk), Sep 10 2004
This sequence does not contain any triangular numbers other than 0 and 1. See A188892. - T. D. Noe, Apr 13 2011
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REFERENCES
| 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
| 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
| a(n)=n*(9*n-7)/2.
G.f.: x*(1+8*x)/(1-x)^3.
Row sums of triangle A131432 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 10 2007
a(n)=9*n+a(n-1)-8 (with a(0)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Aug 06 2010]
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MAPLE
| 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
| s=0; lst={s}; Do[s+=n++ +1; AppendTo[lst, s], {n, 0, 6!, 9}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 15 2008]
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PROG
| (PARI) a(n)=(9*n-7)*n/2 \\ Charles R Greathouse IV, Jun 16 2011
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CROSSREFS
| 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, A000566, A000567, A001106, A001107, 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
| easy,nonn
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AUTHOR
| Barry E. Williams
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EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu), Dec 08 1999
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