OFFSET
1,2
REFERENCES
A. Brousseau, Fibonacci and Related Number Theoretic Tables. Fibonacci Association, San Jose, CA, 1972, p. 19.
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
Index entries for linear recurrences with constant coefficients, signature (6,10,-30,10,6,-1)
FORMULA
a(n) = Sum_{i=0..n} A056571(i).
G.f.: x*(1+x)*(x^2-5*x+1)/ ( (x^2+3*x+1)*(x^2-7*x+1)*(x-1)^2 ). - Ralf Stephan, Apr 23 2004
a(n) = (1/25)*(F(4n+2)-(-1)^n*4*F(2n+1)+6n+3) where F(n)=A000045(n). - Benoit Cloitre, Sep 13 2004. [Corrected by David Lambert (dave.lambert(AT)comcast.net), Mar 28 2008]
MAPLE
with(combinat): l[0] := 0: for i from 1 to 50 do l[i] := l[i-1]+fibonacci(i)^4; printf(`%d, `, l[i]) od: # James A. Sellers, May 29 2000
A005969:=(z+1)*(z**2-5*z+1)/(z**2-7*z+1)/(z**2+3*z+1)/(z-1)**2; # Simon Plouffe in his 1992 dissertation, offset zero
MATHEMATICA
CoefficientList[Series[(1+x)*(x^2-5*x+1)/((x^2+3*x+1)*(x^2-7*x+1)*(x- 1)^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jun 02 2017 *)
LinearRecurrence[{6, 10, -30, 10, 6, -1}, {1, 2, 18, 99, 724, 4820}, 30] (* G. C. Greubel, Jan 17 2018 *)
PROG
(PARI) a(n)=([0, 1, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0; 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 1; -1, 6, 10, -30, 10, 6]^n*[0; 1; 2; 18; 99; 724])[1, 1] \\ Charles R Greathouse IV, Sep 28 2015
(Magma) [(1/25)*(Fibonacci(4*n+2)-(-1)^n*4*Fibonacci(2*n+1)+6*n+3): n in [1..25]]; // Vincenzo Librandi, Jun 02 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from James A. Sellers, May 29 2000
STATUS
approved