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Search: id:A006504
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| A006504 |
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Coefficient of x^4 in (1-x-x^2 )^-n.
(Formerly M3895)
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+0
5
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| 5, 20, 51, 105, 190, 315, 490, 726, 1035, 1430, 1925, 2535, 3276, 4165, 5220, 6460, 7905, 9576, 11495, 13685, 16170, 18975, 22126, 25650, 29575, 33930, 38745, 44051, 49880
(list; graph; listen)
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OFFSET
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1,1
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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.
G. E. Bergum and V. E. Hoggatt, Jr., Numerator polynomial coefficient array for the convolved Fibonacci sequence, Fib. Quart., 14 (1976), 43-48.
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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.
P. Moree, Convoluted convolved Fibonacci numbers
Pieter Moree, Convoluted Convolved Fibonacci Numbers, Journal of Integer Sequences, Vol. 7 (2004), Article 04.2.2.
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FORMULA
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The coefficient of x^4 in (1-x-x^2)^{-n} is the coefficient of x^4 in (1+x+2x^2+3x^3+5x^4)^n. Using the multinomial theorem one then finds that a(n)=7n/4+59*n^2/24+3*n^3/4+n^4/24 - Pieter Moree (moree(AT)science.uva.nl), Sep 03 2003
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MAPLE
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A006504:=-(5-5*z+z**2)/(z-1)**5; [Conjectured by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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Sequence in context: A134481 A062158 A034133 this_sequence A007045 A102227 A006010
Adjacent sequences: A006501 A006502 A006503 this_sequence A006505 A006506 A006507
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KEYWORD
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nonn
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AUTHOR
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njas
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