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A282852
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37-gonal numbers: a(n) = n*(35*n-33)/2.
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1
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0, 1, 37, 108, 214, 355, 531, 742, 988, 1269, 1585, 1936, 2322, 2743, 3199, 3690, 4216, 4777, 5373, 6004, 6670, 7371, 8107, 8878, 9684, 10525, 11401, 12312, 13258, 14239, 15255, 16306, 17392, 18513, 19669, 20860, 22086, 23347, 24643, 25974
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OFFSET
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0,3
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COMMENTS
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According to the common formula for the polygonal numbers: (s-2)*n*(n-1)/2 + n (here s = 37).
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LINKS
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FORMULA
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G.f.: x*(1 + 34*x)/(1 - x)^3.
E.g.f.: exp(x)*(x + 35*x^2/2). (End)
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MATHEMATICA
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Table[n(35n-33)/2, {n, 40}]
PolygonalNumber[37, Range[0, 40]] (* Requires Mathematica version 10 or later *) (* or *) LinearRecurrence[{3, -3, 1}, {0, 1, 37}, 40] (* Harvey P. Dale, Oct 24 2020 *)
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PROG
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(Python)
for n in range(0, 51):
... print(n*(35*n-33)/2)
(PARI) for(n=0, 100, print1(n*(35*n-33)/2, ", ")) \\ Derek Orr, Feb 27 2017
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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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STATUS
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approved
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