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A005971
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Sum of cubes of Lucas numbers.
(Formerly M5198)
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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| A. Brousseau, Fibonacci and Related Number Theoretic Tables. Fibonacci Association, San Jose, CA, 1972, p. 21.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| 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
| 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
| 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
| Sequence in context: A044215 A044596 A192256 * A189808 A130085 A130281
Adjacent sequences: A005968 A005969 A005970 * A005972 A005973 A005974
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms and Maple program from James A. Sellers (sellersj(AT)math.psu.edu), May 29 2000
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