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A129863
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Sums of three consecutive pentagonal numbers.
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5
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6, 18, 39, 69, 108, 156, 213, 279, 354, 438, 531, 633, 744, 864, 993, 1131, 1278, 1434, 1599, 1773, 1956, 2148, 2349, 2559, 2778, 3006, 3243, 3489, 3744, 4008, 4281, 4563, 4854, 5154, 5463, 5781, 6108, 6444, 6789, 7143, 7506, 7878, 8259, 8649, 9048, 9456
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OFFSET
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0,1
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COMMENTS
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Arises in pentagonal number analog to A129803, Triangular numbers that are the sum of three consecutive triangular numbers. What are the pentagonal numbers which are the sum of three consecutive pentagonal numbers?
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LINKS
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FORMULA
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a(n) = P(n) + P(n+1) + P(n+2) where P(n) = A000326(n) = n(3n-1)/2.
a(n) = (9/2)*(n^2) + (15/2)*n + 6.
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EXAMPLE
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MATHEMATICA
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CoefficientList[Series[3 (2 + x^2) / (1 - x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Aug 16 2017 *)
Total/@Partition[PolygonalNumber[5, Range[0, 50]], 3, 1] (* Requires Mathematica version 10 or later *) (* or *) LinearRecurrence[{3, -3, 1}, {6, 18, 39}, 50] (* Harvey P. Dale, Nov 22 2018 *)
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PROG
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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