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A005972
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Partial sums of fourth powers of Lucas numbers.
(Formerly M5358)
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1
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1, 82, 338, 2739, 17380, 122356, 829637, 5709318, 39071494, 267958135, 1836197336, 12586569192, 86266785673, 591288786874, 4052734152890, 27777904133691, 190392453799372, 1304969641560028, 8944394070807629
(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+76x-164x^2-79x^3+16x^4]/[(1-x)^2(1+3x+x^2)(1-7x+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)^4; printf(`%d, `, l[i]) od:
A005972:=(1+76*z-164*z**2-79*z**3+16*z**4)/(z**2-7*z+1)/(z**2+3*z+1)/(z-1)**2; [Conjectured by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| Accumulate[LucasL[Range[20]]^4] (* From Harvey P. Dale, Jul 17 2011 *)
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CROSSREFS
| Sequence in context: A116341 A102956 A031696 * A082972 A031422 A186688
Adjacent sequences: A005969 A005970 A005971 * A005973 A005974 A005975
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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
Clarified definition -- Harvey P. Dale, Jul 17 2011
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