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A145920
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List of numbers that are both pentagonal (A000326) and binomial coefficients C(n,4) (A000332).
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5
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0, 1, 5, 35, 70, 210, 330, 715, 1001, 1820, 2380, 3876, 4845, 7315, 8855, 12650, 14950, 20475, 23751, 31465, 35960, 46376, 52360, 66045, 73815, 91390, 101270, 123410, 135751, 163185, 178365, 211876, 230300, 270725, 292825, 341055, 367290, 424270
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OFFSET
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1,3
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COMMENTS
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All binomial coefficients C(n,4) belong to the generalized pentagonal sequence (A001318).
Pentagonal numbers of generalized pentagonal number (A001318) index number. - Raphie Frank, Nov 25 2012
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LINKS
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FORMULA
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Positive values of A000332(n) belong to the sequence if and only if 3 does not divide n. A000332(n) is positive when n>3.
Conjecture: a(n) = a(n-1) + 4a(n-2) - 4a(n-3) - 6a(n-4) + 6a(n-5) + 4a(n-6) - 4a(n-7) - a(n-8) + a(n-9). - R. J. Mathar, Oct 29 2008
Conjecture: G.f.: x^2(1 + 4x + 26x^2 + 19x^3 + 4x^5 + x^6 + 26x^4)/((1+x)^4(1-x)^5). - R. J. Mathar, Oct 29 2008
a(n) = (27x^4 - 18x^3 - 3x^2 + 2x)/8 where x = floor(n/2)*(-1)^n, for n >= 1. - William A. Tedeschi, Aug 16 2010
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EXAMPLE
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CROSSREFS
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Cf. A141919, of which this is a subsequence.
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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