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Search: id:A145920
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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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+0
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
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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All binomial cofficients C (n, 4) belong to the generalized pentagonal sequence (A001318).
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LINKS
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Eric Weisstein's World of Mathematics, Pentagonal Number.
Eric Weisstein's World of Mathematics, Pentatope Number.
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FORMULA
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a(n+1) = A000326 (A001318(n)).
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). Conjecture: G.f.: x^2(1+4x+26x^2+19x^3+4x^5+x^6+26x^4)/((1+x)^4(1-x)^5). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 29 2008]
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EXAMPLE
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35, for example, is both A000326(5) and A000332(7).
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CROSSREFS
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Cf. A141919, of which this is a subsequence.
Sequence in context: A117985 A115707 A117793 this_sequence A153785 A090294 A162540
Adjacent sequences: A145917 A145918 A145919 this_sequence A145921 A145922 A145923
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KEYWORD
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easy,nonn
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AUTHOR
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Matthew Vandermast (ghodges14(AT)comcast.net), Oct 28 2008
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