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A005056
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a(n) = 3^n + 2^n - 1.
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11
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1, 4, 12, 34, 96, 274, 792, 2314, 6816, 20194, 60072, 179194, 535536, 1602514, 4799352, 14381674, 43112256, 129271234, 387682632, 1162785754, 3487832976, 10462450354, 31385253912, 94151567434, 282446313696, 847322163874, 2541932937192, 7625731702714
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OFFSET
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0,2
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COMMENTS
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Let P(A) be the power set of an n-element set A and R be a relation on P(A) such that for all x, y of P(A), xRy if either 0) x is a proper subset of y or y is a proper subset of x and x and y are disjoint, 1) x is not a subset of y and y is not a subset of x and x and y are disjoint, or 2) x equals y. Then a(n) = |R|. - Ross La Haye, Mar 19 2009
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LINKS
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FORMULA
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G.f.: (1-2x-x^2)/((1-x)(1-2x)(1-3x)).
E.g.f.: exp(3x) + exp(2x) - exp(x). (End)
a(n) = 5*a(n-1) - 6*a(n-2) - 2 for n > 1, a(0)=1, a(1)=4. - Vincenzo Librandi, Dec 31 2010
a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) for n > 2, a(0)=1, a(1)=4, a(2)=12. - Rick L. Shepherd, Aug 07 2017
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MATHEMATICA
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CoefficientList[Series[(1 - 2 x - x^2) / ((1 - x) (1 - 2 x) (1 - 3 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 08 2013 *)
LinearRecurrence[{6, -11, 6}, {1, 4, 12}, 30] (* Harvey P. Dale, Aug 18 2023 *)
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PROG
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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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