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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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FORMULA
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a(n) = n*(9*n+7)/2.
G.f.: x*(8 + x)/(1 - x)^3.
a(n) = Sum_{i=0..n-1} A017257(i) for n > 0. (End)
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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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LinearRecurrence[{3, -3, 1}, {0, 8, 25}, 50] (* Harvey P. Dale, Sep 06 2019 *)
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PROG
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(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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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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