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A177881
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Partial sums of round(3^n/10).
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1
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0, 0, 1, 4, 12, 36, 109, 328, 984, 2952, 8857, 26572, 79716, 239148, 717445, 2152336, 6457008, 19371024, 58113073, 174339220, 523017660, 1569052980, 4707158941, 14121476824, 42364430472, 127093291416
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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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G.f.: x^2/((1 - x)*(1 - 3*x)*(1 + x^2)).
a(n) = round((3*3^n - 3)/20) = round((3*3^n - 5)/20).
a(n) = floor((3*3^n - 1)/20).
a(n) = ceiling((3*3^n - 9)/20).
a(n) = a(n-4) + 4*3^(n-3), n > 3.
a(n) = 4*a(n-1) - 4*a(n-2) + 4*a(n-3) - 3*a(n-4), n > 3.
a(n) = (3^(n+1) + (3 - (-1)^n)*i^(n*(n+1)) - 5)/20, where i = sqrt(-1) - Bruno Berselli, May 12 2021
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EXAMPLE
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a(4) = 0 + 0 + 1 + 3 + 8 = 12.
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MAPLE
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A177881 := proc(n) add( round(3^i/10), i=0..n) ; end proc:
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MATHEMATICA
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Table[(3^(n + 1) + (3 - (-1)^n) i^(n (n + 1)) - 5)/20, {n, 0, 25}] (* Bruno Berselli, May 12 2021 *)
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PROG
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CROSSREFS
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Cf. A015577 (bisection of round(3^n/10)).
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KEYWORD
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nonn,less,easy
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AUTHOR
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STATUS
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approved
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