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A004138
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From a counter moving problem.
(Formerly M0872)
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1
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1, 2, 3, 8, 13, 24, 37, 66, 107, 186, 303, 516, 849, 1436, 2377, 3998, 6639, 11134, 18531, 31024, 51701, 86464, 144205, 241018, 402163, 671906, 1121463, 1873244, 3127129, 5222724, 8719537, 14561622, 24312695, 40600230, 67790379, 113201160, 189016701, 315627944, 527024245, 880037810, 1469467515
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listen;
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OFFSET
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1,2
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REFERENCES
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D. St. P. Barnard, 50 Observer Brain Twisters. Faber and Faber, London, 1962, p. 38.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(n) = a(n-1) + a(n-2) - a(n-3) + 2*a(n-4) + 2 for n >= 5. [Rawlins]
G.f. = -(-1+z^2-4*z^3+2*z^4)/((z-1)*(2*z^4-z^3+z^2+z-1)). [Conjectured (correctly) by Simon Plouffe in his 1992 dissertation.]
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MAPLE
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f:=proc(n) option remember;
if n <= 3 then n
elif n=4 then 8
else 2+f(n-1)+f(n-2)-f(n-3)+2*f(n-4); fi; end;
[seq(f(n), n=1..60)];
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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