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A155020
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a(n) = 2*a(n-1)+2*a(n-2), n>2 ; a(0)=1, a(1)=1, a(2)=3.
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1
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1, 1, 3, 8, 22, 60, 164, 448, 1224, 3344, 9136, 24960, 68192, 186304, 508992, 1390592, 3799168, 10379520, 28357376, 77473792, 211662336, 578272256, 1579869184, 4316282880, 11792304128, 32217174016
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n) is the number of ways to arrange 1 and 2 cent postage stamps in a row so that the first stamp is properly placed (right side up) and any subsequent stamp may (or not) be placed upside down.
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FORMULA
| G.f.: (1-x-x^2)/(1-2*x-2*x^2).
a(n+1) = Sum_{k, 0<=k<=n} A154929(n,k) = A028859(n).
a(n) = (1/3)*sqrt(3)*{[1+sqrt(3)]^(n-1)-[1-sqrt(3)]^(n-1)}+(1/2) *{[1+sqrt(3)]^(n-1)+[1-sqrt(3)]^(n-1)} +(1/2)*[C(2*n,n) mod 2], with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Jan 26 2009]
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EXAMPLE
| a(3) = 8 because we can order the stamps in eight ways:
{1,1,1} {1,1,_1} {1,_1,1} {1,_1,_1} {2,1} {2,_1} {1,2} {1,_2}. Where _1 and _2 are upside down stamps.
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MATHEMATICA
| CoefficientList[Series[(1 - x - x^2)/(1 - 2 x - 2 x^2), {x, 0, 20}], x]
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CROSSREFS
| Equals 1 followed by A028859. [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 18 2009]
Sequence in context: A055887 A024581 A028859 * A014397 A048503 A200752
Adjacent sequences: A155017 A155018 A155019 * A155021 A155022 A155023
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KEYWORD
| nonn
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 19 2009
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