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A087463
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Generalized multiplicative Jacobsthal sequence.
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3
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0, 1, 1, 0, 5, 11, 0, 43, 85, 0, 341, 683, 0, 2731, 5461, 0, 21845, 43691, 0, 174763, 349525, 0, 1398101, 2796203, 0, 11184811, 22369621, 0, 89478485, 178956971, 0, 715827883, 1431655765, 0, 5726623061, 11453246123, 0, 45812984491, 91625968981, 0
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OFFSET
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0,5
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COMMENTS
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2^n = A087462(n) + a(n) + A087464(n) provides a decomposition of Pascal's triangle.
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} if (mod(n*k, 3)=1, 1, 0)*C(n, k).
a(n) = (2/9)*(1-cos(2*Pi*n/3))*(2^n-(-1)^n).
a(n) = 7*a(n-3)+8*a(n-6) for n>5.
G.f.: -x*(4*x^4-2*x^3+x+1) / ((x+1)*(2*x-1)*(x^2-x+1)*(4*x^2+2*x+1)).
(End)
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PROG
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(PARI) concat(0, Vec(-x*(4*x^4-2*x^3+x+1)/((x+1)*(2*x-1)*(x^2-x+1)*(4*x^2+2*x+1)) + O(x^100))) \\ Colin Barker, Nov 02 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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