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A080961
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Fourth binomial transform of A010686 (period 2: repeat 1,5).
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5
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1, 9, 57, 321, 1713, 8889, 45417, 230001, 1158753, 5820009, 29178777, 146130081, 731358993, 3658920729, 18300980937, 91524036561, 457677578433, 2288560079049, 11443316955897, 57218134461441, 286095321353073
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = 5*a(n-1) + 4*3^(n-1).
a(n) = 3*5^n - 2*3^n.
a(n) = Sum_{k=0..n} A003948(n-k)*3^k = Sum_{k=0..n} (3^k * ceiling(Sum_{v=0..n-k} (5^v - 5^(v-2)))). (End)
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EXAMPLE
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G.f. = 1 + 9*x + 57*x^2 + 321*x^3 + 1713*x^4 + 8889*x^5 + 45417*x^6 + 230001*x^7 + ...
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MAPLE
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MATHEMATICA
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CoefficientList[Series[(1 + x)/((1 - 3*x) * (1 - 5*x)), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 07 2012 *)
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PROG
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(Magma) binomtf:=func< V | [ &+[ Binomial(i-1, k-1)*V[k]: k in [1..i] ]: i in [1..#V] ] >;
binomtf(binomtf(binomtf(binomtf(&cat[ [1, 5]: n in [1..11] ])))); // Klaus Brockhaus, Nov 26 2009
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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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EXTENSIONS
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STATUS
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approved
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