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Search: id:A003522
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| A003522 |
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Sum_{k=0..n} C(n-k,3k).
(Formerly M1391)
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+0
5
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| 1, 1, 1, 1, 2, 5, 11, 21, 37, 64, 113, 205, 377, 693, 1266, 2301, 4175, 7581, 13785, 25088, 45665, 83097, 151169, 274969, 500162, 909845, 1655187, 3011157, 5477917, 9965312, 18128529, 32978725, 59993817, 109139117, 198543154
(list; graph; listen)
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OFFSET
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0,5
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REFERENCES
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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.
A. Brousseau, Fibonacci and Related Number Theoretic Tables. Fibonacci Association, San Jose, CA, 1972, p. 113.
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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-x)^2/(1-3x+3x^2-x^3-x^4); a(n)=3a(n-1)-3a(n-2)+a(n-3)+a(n-4). - Paul Barry (pbarry(AT)wit.ie), Jul 07 2004
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MAPLE
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A003522:=-(z-1)**2/(-1+3*z-3*z**2+z**4+z**3); [Conjectured by S. Plouffe in his 1992 dissertation.]
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PROGRAM
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(PARI) a(n)=if(n<0, 0, polcoeff((1-x)^2/(1-3*x+3*x^2-x^3-x^4)+x*O(x^n), n)) /* Michael Somos Sep 20 2005 */
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CROSSREFS
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Sequence in context: A100134 A137356 A103198 this_sequence A112805 A119970 A082775
Adjacent sequences: A003519 A003520 A003521 this_sequence A003523 A003524 A003525
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KEYWORD
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nonn
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AUTHOR
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njas
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