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Search: id:A005971
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| A005971 |
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Sum of cubes of Lucas numbers.
(Formerly M5198)
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+0
1
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| 1, 28, 92, 435, 1766, 7598, 31987, 135810, 574786, 2435653, 10316252, 43702500, 185123261, 784200368, 3321916912, 14071880655, 59609419066, 252509590018, 1069647725567, 4531100578950, 19194049901126, 81307300410353
(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).
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. Brousseau, Fibonacci and Related Number Theoretic Tables. Fibonacci Association, San Jose, CA, 1972, p. 21.
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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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G.f.: [1+24x-23x^2-8x^3]/[(1-x)(1+x-x^2)(1-4x-x^2)]. - Ralf Stephan, Apr 23 2004
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MAPLE
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lucas := proc(n) option remember: if n=1 then RETURN(1) fi: if n=2 then RETURN(3) fi: lucas(n-1)+lucas(n-2) end: l[0] := 0: for i from 1 to 50 do l[i] := l[i-1]+lucas(i)^3; printf(`%d, `, l[i]) od:
A005971:=(-1-24*z+23*z**2+8*z**3)/(z-1)/(z**2+4*z-1)/(z**2-z-1); [Conjectured by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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Sequence in context: A113958 A044215 A044596 this_sequence A130085 A130281 A010016
Adjacent sequences: A005968 A005969 A005970 this_sequence A005972 A005973 A005974
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KEYWORD
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nonn
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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 and Maple program from James A. Sellers (sellersj(AT)math.psu.edu), May 29 2000
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