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Search: id:A006564
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| A006564 |
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Icosahedral numbers: n(5n^2 -5n + 2)/2.
(Formerly M4837)
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+0
7
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| 1, 12, 48, 124, 255, 456, 742, 1128, 1629, 2260, 3036, 3972, 5083, 6384, 7890, 9616, 11577, 13788, 16264, 19020, 22071, 25432, 29118, 33144, 37525, 42276, 47412, 52948, 58899
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Schlaefli symbol for this polyhedron: {3,5}
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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).
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.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
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.
Hyun Kwang Kim, On Regular Polytope Numbers
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FORMULA
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a(n) = C(n+2,3) + 8 C(n+1,3) + 6 C(n,3)
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MAPLE
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A006564:=(1+8*z+6*z**2)/(z-1)**4; [Conjectured by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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Cf. A000292, A000578, A005900, A006566
Sequence in context: A009958 A135453 A165280 this_sequence A059162 A117027 A161171
Adjacent sequences: A006561 A006562 A006563 this_sequence A006565 A006566 A006567
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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