OFFSET
1,2
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).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Kunle Adegoke, Sums of fourth powers of Fibonacci and Lucas numbers, arXiv:1706.00407 [math.NT], 2017.
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
FORMULA
G.f.: x*(1+76*x-164*x^2-79*x^3+16*x^4)/((1-x)^2*(1+3*x+x^2)*(1-7*x+x^2)). - Ralf Stephan, Apr 23 2004
a(n) = A000045(4*n+2) + 4*(-1)^n*(A000045(n)^2 + A000045(n+1)^2) + 6*n-5. - Vaclav Kotesovec, Nov 19 2012
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: # James A. Sellers, May 29 2000
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; # Simon Plouffe in his 1992 dissertation
MATHEMATICA
Accumulate[LucasL[Range[20]]^4] (* Harvey P. Dale, Jul 17 2011 *)
Table[Fibonacci[4*n+2]+(-1)^n*(4*Fibonacci[n]^2+4*Fibonacci[n+1]^2)+6*n-5, {n, 1, 20}] (* Vaclav Kotesovec, Nov 19 2012 *)
CoefficientList[Series[(1 + 76 x - 164 x^2 - 79 x^3 + 16 x^4) / ((1 - x)^2 (1 + 3 x + x^2) (1 - 7 x + x^2)), {x, 0, 30}], x] (* Vincenzo Librandi, May 03 2012 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from James A. Sellers, May 29 2000
Definition clarified by Harvey P. Dale, Jul 17 2011
STATUS
approved