|
Search: id:A005972
|
|
|
| A005972 |
|
Sum of fourth powers of Lucas numbers.
(Formerly M5358)
|
|
+0
1
|
|
| 1, 82, 338, 2739, 17380, 122356, 829637, 5709318, 39071494, 267958135, 1836197336, 12586569192, 86266785673, 591288786874, 4052734152890, 27777904133691, 190392453799372, 1304969641560028, 8944394070807629
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
REFERENCES
|
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
A. Brousseau, Fibonacci and Related Number Theoretic Tables. Fibonacci Association, San Jose, CA, 1972, p. 21.
|
|
LINKS
|
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
|
|
FORMULA
|
G.f.: [1+76x-164x^2-79x^3+16x^4]/[(1-x)^2(1+3x+x^2)(1-7x+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)^4; printf(`%d, `, l[i]) od:
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; [Conjectured by S. Plouffe in his 1992 dissertation.]
|
|
CROSSREFS
|
Sequence in context: A116341 A102956 A031696 this_sequence A082972 A031422 A002309
Adjacent sequences: A005969 A005970 A005971 this_sequence A005973 A005974 A005975
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
njas
|
|
EXTENSIONS
|
More terms and Maple program from James A. Sellers (sellersj(AT)math.psu.edu), May 29 2000
|
|
|
Search completed in 0.004 seconds
|
