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A086953
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Binomial transform of (-1)^mod(n,3) (A257075).
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2
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1, 0, 0, 2, 6, 12, 22, 42, 84, 170, 342, 684, 1366, 2730, 5460, 10922, 21846, 43692, 87382, 174762, 349524, 699050, 1398102, 2796204, 5592406, 11184810, 22369620, 44739242, 89478486, 178956972, 357913942, 715827882, 1431655764, 2863311530, 5726623062
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OFFSET
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0,4
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LINKS
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FORMULA
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a(n) = 0^n + Sum{k=0..floor((n-1)/3)} C(n-1, 3*k+2).
a(n) = Sum{k=0..n} C(n, k)(-1)^mod(k, 3).
G.f.: (1 - 3*x + 3*x^2)/((1 - 2*x)*(1 - x + x^2)). - Paul Barry, Dec 14 2004
a(n) = A024495(n) if and only if n == 1 (mod 3);
a(n) = A024495(n) - 1 if and only if n == 2 or 3 (mod 6);
a(n) = A024495(n) + 1 if and only if n == 0 or 5 (mod 6);
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MATHEMATICA
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LinearRecurrence[{3, -3, 2}, {1, 0, 0}, 40] (* Harvey P. Dale, Aug 02 2017 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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