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Search: id:A002419
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| A002419 |
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4-dimensional figurate numbers: (6n-2)*C(n+2,3)/4.
(Formerly M4699 N2008)
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+0
6
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| 1, 10, 40, 110, 245, 476, 840, 1380, 2145, 3190, 4576, 6370, 8645, 11480, 14960, 19176, 24225, 30210, 37240, 45430, 54901, 65780, 78200, 92300, 108225, 126126, 146160, 168490, 193285, 220720, 250976, 284240, 320705, 360570, 404040, 451326
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 195.
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LINKS
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
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a(n)= (3*n-1)*binomial(n+2, 3)/2, n>=1. G.f.: x*(1+5*x)/(1-x)^5.
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MAPLE
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A002419:=-(1+5*z)/(z-1)**5; [Conjectured by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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Cf. A093563 ((6, 1) Pascal, column m=4). A002414 (differences).
Sequence in context: A131037 A071233 A063490 this_sequence A027981 A013977 A075060
Adjacent sequences: A002416 A002417 A002418 this_sequence A002420 A002421 A002422
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Pab Ter (pabrlos(AT)yahoo.com), May 08 2004
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