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A001641
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A Fielder sequence.
(Formerly M2364 N0935)
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2
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1, 3, 4, 11, 16, 30, 50, 91, 157, 278, 485, 854, 1496, 2628, 4609, 8091, 14196, 24915, 43720, 76726, 134642, 236283, 414645, 727654, 1276941, 2240878, 3932464, 6900996, 12110401, 21252275, 37295140, 65448411, 114853952, 201554638
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| Fielder, Daniel C.; Special integer sequences controlled by three parameters. Fibonacci Quart 6 1968 64-70.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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.
Y. Puri and T. Ward, Arithmetic and growth of periodic orbits, J. Integer Seqs., Vol. 4 (2001), #01.2.1.
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FORMULA
| G.f.: x*(1+2*x+4*x^3)/(1-x-x^2-x^4).
a(n)=n*sum(k=1..n, sum(j=floor((4*k-n)/3)..floor((4*k-n)/2), binomial(j,n-4*k+3*j)*binomial(k,j))/k). [From Vladimir Kruchinin (kru(AT)ie.tusur.ru), May 25 2011]
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MAPLE
| A001641:=-(1+2*z+4*z**3)/(z+1)/(z**3-z**2+2*z-1); [Conjectured by S. Plouffe in his 1992 dissertation.]
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PROG
| (PARI) a(n)=if(n<0, 0, polcoeff(x*(1+2*x+4*x^3)/(1-x-x^2-x^4)+x*O(x^n), n))
a(n):=(sum(sum(binomial(j, n-4*k+3*j)*binomial(k, j), j, floor((4*k-n)/3), floor((4*k-n)/2))/k, k, 1, n))*n; [From Vladimir Kruchinin (kru(AT)ie.tusur.ru), May 25 2011]
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CROSSREFS
| Cf. A060945.
Sequence in context: A116654 A041020 A041527 * A007382 A127804 A027306
Adjacent sequences: A001638 A001639 A001640 * A001642 A001643 A001644
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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