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A097038
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A Jacobsthal variant.
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3
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0, 1, 1, 5, 7, 21, 35, 85, 155, 341, 651, 1365, 2667, 5461, 10795, 21845, 43435, 87381, 174251, 349525, 698027, 1398101, 2794155, 5592405, 11180715, 22369621, 44731051, 89478485, 178940587, 357913941, 715795115, 1431655765, 2863245995
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OFFSET
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0,4
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COMMENTS
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LINKS
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FORMULA
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G.f.: 1/(1-x-2*x^2) - 1/(1-2*x^2) = x/((1-2*x^2)*(1-x-2*x^2));
a(n) = 2*2^n/3+(-1)^n/3-2^(n/2)*(1+(-1)^n)/2;
a(n) = sum{k=0..floor((n+1)/2), binomial(n-k+1, k-1)2^k };
a(n) = sum{k=0..n, 2^(k/2)(1+(-1)^k)A001045(n-k)/2 };
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PROG
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(PARI) concat(0, Vec(x/((1-2*x^2)*(1-x-2*x^2)) + O(x^50))) \\ Michel Marcus, Nov 13 2015
(PARI) vector(50, n, n--; 2*2^n/3+(-1)^n/3-2^(n/2)*(1+(-1)^n)/2) \\ Altug Alkan, Nov 13 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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