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A003522
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Sum_{k=0..n} C(n-k,3k).
(Formerly M1391)
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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; refs; listen; history; internal format)
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OFFSET
| 0,5
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REFERENCES
| A. Brousseau, Fibonacci and Related Number Theoretic Tables. Fibonacci Association, San Jose, CA, 1972, p. 113.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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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.
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FORMULA
| 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
| 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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PROG
| (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
| Sequence in context: A137356 A103198 A183929 * A112805 A119970 A082775
Adjacent sequences: A003519 A003520 A003521 * A003523 A003524 A003525
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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