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A062728
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Second 11-gonal (or hendecagonal) numbers: a(n) = n*(9*n+7)/2.
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15
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0, 8, 25, 51, 86, 130, 183, 245, 316, 396, 485, 583, 690, 806, 931, 1065, 1208, 1360, 1521, 1691, 1870, 2058, 2255, 2461, 2676, 2900, 3133, 3375, 3626, 3886, 4155, 4433, 4720, 5016, 5321, 5635, 5958, 6290, 6631, 6981, 7340, 7708, 8085, 8471, 8866, 9270
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OFFSET
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0,2
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COMMENTS
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Old name: 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 0,8,...
Sequence found by reading the line from 0, in the direction 0, 25, ... and the line from 8, in the direction 8, 51, ..., in the square spiral whose vertices are the generalized 11-gonal numbers A195160. - Omar E. Pol, Jul 24 2012
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LINKS
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Ivan Panchenko, Table of n, a(n) for n = 0..1000
Index entries for 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.
a(n) = 9*n + a(n-1) - 1 (with a(0)=0). - Vincenzo Librandi, Aug 07 2010
From Bruno Berselli, Jan 13 2011: (Start)
G.f.: x*(8 + x)/(1 - x)^3.
a(n) = Sum_{i=0..n-1} A017257(i) for n > 0. (End)
a(n) = A218470(9n+7). - Philippe Deléham, Mar 27 2013
E.g.f.: x*(16 + 9*x)*exp(x)/2. - G. C. Greubel, May 24 2019
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EXAMPLE
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The spiral begins:
15
/ \
16 14
/ \
17 3 13
/ / \ \
18 4 2 12
/ / \ \
19 5 0---1 11
/ / \
20 6---7---8---9--10
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MATHEMATICA
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Table[n*(9*n+7)/2, {n, 0, 50}] (* G. C. Greubel, May 24 2019 *)
LinearRecurrence[{3, -3, 1}, {0, 8, 25}, 50] (* Harvey P. Dale, Sep 06 2019 *)
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PROG
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(PARI) a(n)=n*(9*n+7)/2 \\ Charles R Greathouse IV, Jun 17 2017
(MAGMA) [n*(9*n+7)/2: n in [0..50]]; // G. C. Greubel, May 24 2019
(Sage) [n*(9*n+7)/2 for n in (0..50)] # G. C. Greubel, May 24 2019
(GAP) List([0..50], n-> n*(9*n+7)/2) # G. C. Greubel, May 24 2019
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CROSSREFS
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Cf. A051682.
Second n-gonal numbers: A005449, A014105, A147875, A045944, A179986, A033954, this sequence, A135705.
Sequence in context: A089613 A164754 A204467 * A273982 A244942 A143371
Adjacent sequences: A062725 A062726 A062727 * A062729 A062730 A062731
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KEYWORD
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nonn,easy
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AUTHOR
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Floor van Lamoen, Jul 21 2001
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EXTENSIONS
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New name from Bruno Berselli (with the original formula), Jan 13 2011
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STATUS
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approved
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