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Search: id:A000297
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| A000297 |
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(n+1)*(n+3)*(n+8)/6.
(Formerly M3434 N1393)
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+0
5
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| 0, 4, 12, 25, 44, 70, 104, 147, 200, 264, 340, 429, 532, 650, 784, 935, 1104, 1292, 1500, 1729, 1980, 2254, 2552, 2875, 3224, 3600, 4004, 4437, 4900, 5394, 5920, 6479, 7072, 7700, 8364, 9065, 9804, 10582, 11400, 12259, 13160, 14104, 15092, 16125, 17204
(list; graph; listen)
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OFFSET
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-1,2
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COMMENT
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If Y and Z are 2-blocks of an n-set X then, for n>=4, a(n-5) is the number of (n-3)-subsets of X intersecting both Y and Z. - Milan R. Janjic (agnus(AT)blic.net), Nov 09 2007
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REFERENCES
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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.
P. Erdos, R. K. Guy and J. W. Moon, On refining partitions, J. London Math. Soc., 9 (1975), 565-570.
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 150.
A. Scott, T. Delaney and V. E. Hoggatt, Jr., The tribonacci sequence, Fib. Quart., 15 (1977), 193-200.
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LINKS
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Milan Janjic, Two Enumerative Functions
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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G.f.: (2-x)^2 / (1-x)^4.
a(n)=sum(n*(k+1)/3,k=3..n, n>=2 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 29 2008
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MAPLE
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A000297:=(z-2)**2/(z-1)**4; [Conjectured by S. Plouffe in his 1992 dissertation.]
for n from 2 to 46 do printf(`%d, `, sum(n*(k+1)/3, k=3..n)) od: - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 29 2008
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CROSSREFS
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Sequence in context: A116668 A008186 A008264 this_sequence A078618 A062883 A008176
Adjacent sequences: A000294 A000295 A000296 this_sequence A000298 A000299 A000300
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Sep 08 2000
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