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A132045 Row sums of triangle A132044. 4
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

Table of n, a(n) for n=0..33.

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.: -(2*x^3-2*x+1) / ((x-1)^2*(2*x-1)). (End)

a(0)=1, a(n) = 2^n - n + 1 for n > 0. - Jon E. Schoenfield, Jun 15 2017

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).

PROG

(PARI) Vec(-(2*x^3-2*x+1)/((x-1)^2*(2*x-1)) + O(x^100)) \\ Colin Barker, Mar 14 2014

CROSSREFS

Cf. A095768, A132044.

Sequence in context: A030040 A274493 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 September 20 16:05 EDT 2017. Contains 292276 sequences.