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A132045
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Row sums of triangle A132044.
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7
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1, 2, 3, 6, 13, 28, 59, 122, 249, 504, 1015, 2038, 4085, 8180, 16371, 32754, 65521, 131056, 262127, 524270, 1048557, 2097132, 4194283, 8388586, 16777193, 33554408, 67108839, 134217702, 268435429, 536870884, 1073741795, 2147483618, 4294967265, 8589934560
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OFFSET
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0,2
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COMMENTS
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Apart from initial terms, and with a change of offset, same as A095768. - Jon E. Schoenfield, Jun 15 2017
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-5,2).
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FORMULA
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Binomial transform of (1, 1, 0, 2, 0, 2, 0, 2, 0, 2, ...).
For n>=1, a(n) = 2^n - n + 1 = A000325(n) + 1. - Avik Roy (avik_3.1416(AT)yahoo.co.in), Jan 17 2009. (Corrected by Franklin T. Adams-Watters, Jan 17 2009)
E.g.f.: U(0)- 1, where U(k) = 1 - x/(2^k + 2^k/(x - 1 - x^2*2^(k+1)/(x*2^(k+1) + (k+1)/U(k+1) ))). - Sergei N. Gladkovskii, Dec 01 2012
From Colin Barker, Mar 14 2014: (Start)
a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3) for n>3.
G.f.: (1-2*x+2*x^3) / ((1-x)^2*(1-2*x)). (End)
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EXAMPLE
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a(4) = 13 = sum of row 4 terms of triangle A132044: (1 + 3 + 5 + 3 + 1).
a(4) = 13 = (1, 4, 6, 4, 1) dot (1, 1, 0, 2, 0) = (1 + 4 + 0 + 8 + 0).
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MATHEMATICA
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Table[2^n -(n-1) -Boole[n==0], {n, 0, 35}] (* G. C. Greubel, Feb 12 2021 *)
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PROG
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(PARI) Vec((1-2*x+2*x^3)/((1-x)^2*(1-2*x)) + O(x^100)) \\ Colin Barker, Mar 14 2014
(Sage) [1]+[2^n -n +1 for n in (1..35)] # G. C. Greubel, Feb 12 2021
(Magma) [1] cat [2^n -n +1: n in [1..35]]; // G. C. Greubel, Feb 12 2021
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CROSSREFS
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Cf. A000325, A095768, A132044.
Sequence in context: A274493 A324770 A075853 * A032143 A032160 A089735
Adjacent sequences: A132042 A132043 A132044 * A132046 A132047 A132048
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KEYWORD
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nonn,easy
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AUTHOR
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Gary W. Adamson, Aug 08 2007
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STATUS
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approved
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