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 A132045 Row sums of triangle A132044. 7
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Apart from initial terms, and with a change of offset, same as A095768. - Jon E. Schoenfield, Jun 15 2017 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (4,-5,2). FORMULA 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) EXAMPLE 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). MATHEMATICA Table[2^n -(n-1) -Boole[n==0], {n, 0, 35}] (* G. C. Greubel, Feb 12 2021 *) PROG (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 CROSSREFS Cf. A000325, A095768, A132044. Sequence in context: A274493 A324770 A075853 * A032143 A032160 A089735 Adjacent sequences: A132042 A132043 A132044 * A132046 A132047 A132048 KEYWORD nonn,easy AUTHOR Gary W. Adamson, Aug 08 2007 STATUS approved

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Last modified June 6 04:33 EDT 2023. Contains 363139 sequences. (Running on oeis4.)