login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 6 09:29 EDT 2022. Contains 357263 sequences. (Running on oeis4.)