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A005970
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Sum of squares of Lucas numbers.
(Formerly M4689)
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2
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1, 10, 26, 75, 196, 520, 1361, 3570, 9346, 24475, 64076, 167760, 439201, 1149850, 3010346, 7881195, 20633236, 54018520, 141422321, 370248450, 969323026, 2537720635, 6643838876, 17393796000, 45537549121, 119218851370
(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. 20.
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+7x-4x^2]/[(1-x)(1+x)(1-3x+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)^2; printf(`%d, `, l[i]) od:
A005970:=(-1-7*z+4*z**2)/(z-1)/(z+1)/(z**2-3*z+1); [Conjectured by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
| Sequence in context: A134420 A144255 A072379 * A192254 A051966 A092774
Adjacent sequences: A005967 A005968 A005969 * A005971 A005972 A005973
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KEYWORD
| nonn,easy
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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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