OFFSET
1,2
REFERENCES
Alfred 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; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992.
Index entries for linear recurrences with constant coefficients, signature (3,0,-3,1).
FORMULA
a(n) - a(n-1) = A001254(n).
G.f.: (1+7*x-4*x^2)/((1-x)*(1+x)*(1-3*x+x^2)). - Simon Plouffe in his 1992 dissertation
From Amiram Eldar, Jan 13 2022: (Start)
a(n) = Sum_{k=1..n} L(k)^2, where L(k) is the k-th Lucas number (A000032).
a(n) = 3*a(n-1) - 3*a(n-3) + a(n-4), for n > 4.
a(n) = L(n)*L(n+1) - 2 = A215602(n) - 2. (End)
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
MATHEMATICA
Accumulate[LucasL[Range[30]]^2] (* Harvey P. Dale, Dec 06 2019 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from James A. Sellers, May 29 2000
Definition clarified by Harvey P. Dale, Dec 06 2019
STATUS
approved