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A081654
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a(n) = 2*4^n - 0^n.
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8
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1, 8, 32, 128, 512, 2048, 8192, 32768, 131072, 524288, 2097152, 8388608, 33554432, 134217728, 536870912, 2147483648, 8589934592, 34359738368, 137438953472, 549755813888, 2199023255552, 8796093022208, 35184372088832
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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a(0)=1, a(n) = 2*4^n, n>0
G.f.: (1+4*x)/(1-4*x).
E.g.f. 2*exp(4*x)-1.
With interpolated zeros, this is 2^n - 0^n + (-2)^n. - Paul Barry, Sep 06 2003
For n>0, a(n) = 2 * (1 + 3^(n-1) + Sum{x=1..n-2}Sum{k=0..x-1}(binomial(x-1,k)*(3^(k+1) + 3^(n-x+k)))). - J. Conrad, Dec 10 2015
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EXAMPLE
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a(0) = 2*4^0 - 0^0 = 2 - 1 = 1 (use 0^0 = 1).
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MATHEMATICA
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CoefficientList[Series[(1 + 4 x) / (1 - 4 x), {x, 0, 40}], x] (* Vincenzo Librandi, Aug 10 2013 *)
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PROG
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(PARI) x='x+O('x^100); Vec((1+4*x)/(1-4*x)) \\ Altug Alkan, Dec 14 2015
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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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