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A005970 Partial sums of squares of Lucas numbers.
(Formerly M4689)
3
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; text; internal format)
OFFSET

1,2

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).

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

FORMULA

G.f.: [1+7x-4x^2]/[(1-x)(1+x)(1-3x+x^2)]. - Ralf Stephan, Apr 23 2004

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: # James A. Sellers, May 29 2000

A005970:=(-1-7*z+4*z**2)/(z-1)/(z+1)/(z**2-3*z+1); # conjectured by Simon Plouffe in his 1992 dissertation

MATHEMATICA

Accumulate[LucasL[Range[30]]^2] (* Harvey P. Dale, Dec 06 2019 *)

CROSSREFS

Sequence in context: A144255 A259290 A072379 * A192254 A220155 A321311

Adjacent sequences:  A005967 A005968 A005969 * A005971 A005972 A005973

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from James A. Sellers, May 29 2000

Definition clarified by Harvey P. Dale, Dec 06 2019

STATUS

approved

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Last modified March 28 20:44 EDT 2020. Contains 333103 sequences. (Running on oeis4.)