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Search: id:A005969
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| A005969 |
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Sum of fourth powers of Fibonacci numbers.
(Formerly M2106)
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+0
10
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| 1, 2, 18, 99, 724, 4820, 33381, 227862, 1564198, 10714823, 73457064, 503438760, 3450734281, 23651386922, 162109796922, 1111115037483, 7615701104764, 52198777931900, 357775783071021, 2452231602371646, 16807845698458702
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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A. Brousseau, Fibonacci and Related Number Theoretic Tables. Fibonacci Association, San Jose, CA, 1972, p. 19.
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LINKS
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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.
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FORMULA
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G.f.: [1-4x-4x^2-x^3]/[(1-x)^2(1+3x+x^2)(1-7x+x^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 (benoit7848c(AT)orange.fr), Sep 13 2004. [Corrected by David Lambert (dave.lambert(AT)comcast.net), Mar 28 2008]
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MAPLE
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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:
A005969:=(z+1)*(z**2-5*z+1)/(z**2-7*z+1)/(z**2+3*z+1)/(z-1)**2; [S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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Cf. A001654, A098531, A098532, A098533.
Cf. A119285, A000071, A001654, A005968, A098531, A098532, A098533, A128697.
Adjacent sequences: A005966 A005967 A005968 this_sequence A005970 A005971 A005972
Sequence in context: A127553 A055357 A087291 this_sequence A094251 A101570 A006043
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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EXTENSIONS
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More terms and Maple program from James A. Sellers (sellersj(AT)math.psu.edu), May 29 2000
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