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A297619
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a(n) = 2*a(n-1) + 2*a(n-2) - 4*a(n-3), a(1) = 0, a(2) = 0, a(3) = 8.
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1
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0, 0, 8, 16, 48, 96, 224, 448, 960, 1920, 3968, 7936, 16128, 32256, 65024, 130048, 261120, 522240, 1046528, 2093056, 4190208, 8380416, 16769024, 33538048, 67092480, 134184960, 268402688, 536805376, 1073676288, 2147352576, 4294836224, 8589672448, 17179607040
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OFFSET
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1,3
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COMMENTS
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Number of minimum distinguishing (2-)labelings of the n-pan graph for n >= 3.
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LINKS
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Eric Weisstein's World of Mathematics, Pan Graph
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FORMULA
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a(n) = 2^(n + 1) - 2^(floor(n/2) + 2).
a(n) = 2*(n-1) + 2*a(n-2) - 4*a(n-3).
G.f.: 8*x^3/(1 - 2*x - 2*x^2 + 4*x^3).
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MAPLE
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f := proc(n) option remember:
if n = 1 then 0 elif n = 2 then 0 elif n = 3 then 8 elif n >= 4 then 2 * procname(n-1) + 2* procname(n-2) - 4 * procname(n-3) fi; end:
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MATHEMATICA
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Table[2^(n + 1) - 2^(Floor[n/2] + 2), {n, 20}]
LinearRecurrence[{2, 2, -4}, {0, 0, 8}, 20]
CoefficientList[Series[(8 x^2)/(1 - 2 x - 2 x^2 + 4 x^3), {x, 0, 20}], x]
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PROG
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(PARI) first(n) = Vec(8*x^3/(1 - 2*x - 2*x^2 + 4*x^3) + O(x^(n+1)), -n) \\ Iain Fox, Jan 02 2018
(GAP) a := [0, 0, 8];; for n in [4..500] do a[n] := 2 * a[n-1] + 2 * a[n-2] - 4 * a[n-3]; od; a; # Muniru A Asiru, Jan 28 2018
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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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STATUS
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approved
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