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A226538
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a(2t) = a(2t-1) + 1, a(2t+1) = a(2t) + a(2t-2) for t >= 1, with a(0) = a(1) = 1.
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3
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1, 1, 2, 3, 4, 6, 7, 11, 12, 19, 20, 32, 33, 53, 54, 87, 88, 142, 143, 231, 232, 375, 376, 608, 609, 985, 986, 1595, 1596, 2582, 2583, 4179, 4180, 6763, 6764, 10944, 10945, 17709, 17710, 28655, 28656, 46366, 46367, 75023, 75024, 121391, 121392, 196416, 196417
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = a(n-1) + a(n-3)*(1-(-1)^n)/2 + (1+(-1)^n)/2. - Paolo P. Lava, Jun 27 2013
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MAPLE
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f:= proc(n) option remember;
if n <= 1 then 1
elif n mod 2 = 0 then f(n-1)+1
else f(n-1)+f(n-3)
fi
end:
t21:=[seq(f(n), n=0..60)];
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MATHEMATICA
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LinearRecurrence[{0, 2, 0, 0, 0, -1}, {1, 1, 2, 3, 4, 6}, 50] (* Jean-François Alcover, Feb 13 2018 *)
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PROG
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(Haskell)
a226538 n = a226538_list !! n
a226538_list = concat $ transpose [drop 2 a000071_list, tail a001911_list]
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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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EXTENSIONS
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STATUS
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approved
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