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A081674
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Generalized Poly-Bernoulli numbers.
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3
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0, 1, 6, 29, 130, 561, 2366, 9829, 40410, 164921, 669526, 2707629, 10919090, 43942081, 176565486, 708653429, 2841788170, 11388676041, 45619274246, 182670807229, 731264359650, 2926800830801, 11712433499806, 46865424529029
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OFFSET
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0,3
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COMMENTS
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Number of walks of length 2n+2 between two nodes at distance 4 in the cycle graph C_12. - Herbert Kociemba, Jul 05 2004
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LINKS
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FORMULA
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a(n) = ((4^(n+1) - 1)/3 - 3^n)/2 = (4*4^n - 3*3^n - 1)/6.
G.f.: x*(1-2*x)/((1-x)*(1-3*x)*(1-4*x)).
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MATHEMATICA
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CoefficientList[Series[(x(1-2x))/((1-x)(1-3x)(1-4x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{8, -19, 12}, {0, 1, 6}, 30] (* Harvey P. Dale, Nov 28 2018 *)
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PROG
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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