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 A005972 Partial sums of fourth powers of Lucas numbers. (Formerly M5358) 1
 1, 82, 338, 2739, 17380, 122356, 829637, 5709318, 39071494, 267958135, 1836197336, 12586569192, 86266785673, 591288786874, 4052734152890, 27777904133691, 190392453799372, 1304969641560028, 8944394070807629 (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. 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 Sequence in context: A116341 A102956 A031696 * A082972 A288920 A304416 Adjacent sequences:  A005969 A005970 A005971 * A005973 A005974 A005975 KEYWORD nonn AUTHOR EXTENSIONS More terms from James A. Sellers, May 29 2000 Definition clarified by Harvey P. Dale, Jul 17 2011 STATUS approved

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Last modified May 28 18:24 EDT 2022. Contains 354122 sequences. (Running on oeis4.)