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A062725
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Write 0,1,2,3,4,... in a triangular spiral, then a(n) is the sequence found by reading the terms along the line from 0 in the direction 0,7,...
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7
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0, 7, 23, 48, 82, 125, 177, 238, 308, 387, 475, 572, 678, 793, 917, 1050, 1192, 1343, 1503, 1672, 1850, 2037, 2233, 2438, 2652, 2875, 3107, 3348, 3598, 3857, 4125, 4402, 4688, 4983, 5287, 5600, 5922, 6253, 6593, 6942, 7300, 7667, 8043, 8428, 8822, 9225
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = n*(9*n+5)/2.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: x*(7+2*x)/(1-x)^3. (End)
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EXAMPLE
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The spiral begins:
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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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CoefficientList[Series[x (7 + 2 x)/(1 - x)^3, {x, 0, 45}], x] (* Michael De Vlieger, Jan 11 2020 *)
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PROG
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(Haskell)
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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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Formula that confused indices corrected by R. J. Mathar, Jun 04 2010
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STATUS
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approved
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