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A132736
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Row sums of triangle A132735.
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2
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1, 2, 5, 10, 19, 36, 69, 134, 263, 520, 1033, 2058, 4107, 8204, 16397, 32782, 65551, 131088, 262161, 524306, 1048595, 2097172, 4194325, 8388630, 16777239, 33554456, 67108889, 134217754, 268435483, 536870940, 1073741853, 2147483678
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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Binomial transform of [1, 1, 2, 0, 2, 0, 2, 0, 2, ...].
a(n) = 4*a(n-1) -5*a(n-2) +2*a(n-3) for n>3.
G.f.: (1 -2*x +2*x^2 -2*x^3)/((1-x)^2*(1-2*x)). (End)
a(n) = 2^n + n - 1 + [n=0].
E.g.f.: 1 - (1-x)*exp(x) + exp(2*x). (End)
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EXAMPLE
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a(4) = 19 = sum of row 4 terms of triangle A132735: (1 + 5 + 7 + 5 + 1).
a(3) = 10 = (1, 3, 3, 1) dot (1, 1, 2, 0) = (1 + 3 + 6 + 0).
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MAPLE
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a:= proc(n) option remember; if n=0 then 1 else add((binomial(n, j)+1), j=0..n-1) fi end: seq(a(n), n=0..31); # Zerinvary Lajos, Mar 29 2009
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MATHEMATICA
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Table[2^n + n-1 + Boole[n==0], {n, 0, 30}] (* G. C. Greubel, Feb 14 2021 *)
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PROG
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(Sage) [1]+[2^n + n-1 for n in (1..30)] # G. C. Greubel, Feb 14 2021
(Magma) [1] cat [2^n + n-1: n in [1..30]]; // G. C. Greubel, Feb 14 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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