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A133494 Diagonal of the array of iterated differences of A047848. 14
1, 1, 3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323, 4782969, 14348907, 43046721, 129140163, 387420489, 1162261467, 3486784401, 10460353203, 31381059609, 94143178827, 282429536481, 847288609443, 2541865828329, 7625597484987 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) is the number of ways to choose a composition C, and then choose a composition of each part of C. - Geoffrey Critzer, Mar 19 2012

a(n) is the top left entry of the n-th power of the 3 X 3 matrix [1, 1, 1; 1, 1, 1; 1, 1, 1]. - R. J. Mathar, Feb 03 2014

a(n) is the reptend length of 1/3^(n+1) in decimal. - Jianing Song, Nov 14 2018

LINKS

Table of n, a(n) for n=0..28.

Index entries for linear recurrences with constant coefficients, signature (3).

FORMULA

Binomial transform of A078008. - Paul Curtz, Aug 04 2008

G.f.: (1 - 2x)/(1 - 3x). a(n) = A000244(n-1), n > 0. - R. J. Mathar, Nov 11 2008

a(n) = Sum_{k=0..n} A112467(n,k)*2^k = Sum_{k=0..n} A071919(n,k)*2^k. - Philippe Deléham, Nov 13 2008

Let A(x) be the g.f. Then B(x) = x*A(x) satisfies B(x/(1-x)) = x/(1 - 2*B(x)). - Vladimir Kruchinin, Dec 05 2011

G.f.: 1/(1 - (Sum_{k>=1} (x/(1 - x))^k)). - Joerg Arndt, Sep 30 2012

For n > 0, a(n) = 2*(Sum_{k=0..n-1} a(k)) - 1 = 3^(n-1). - J. Conrad, Oct 29 2015

G.f.: 1 + x/(1 + x)*(1 + 4*x/(1 + 4*x)*(1 + 7*x/(1 + 7*x)*(1 + 10*x/(1 + 10*x)*(1 + .... - Peter Bala, May 27 2017

MATHEMATICA

CoefficientList[Series[(1 - 2 x)/(1 - 3 x), {x, 0, 50}], x] (* Vladimir Joseph Stephan Orlovsky, Jun 21 2011 *)

PROG

(PARI) a(n)=max(1, 3^(n-1)) \\ Charles R Greathouse IV, Jul 07 2011

(PARI) Vec((1-2*x)/(1-3*x) + O(x^100)) \\  Altug Alkan, Oct 30 2015

CROSSREFS

Cf. A182105.

Sequence in context: A140429 A141413 A000244 * A050733 A238939 A079846

Adjacent sequences:  A133491 A133492 A133493 * A133495 A133496 A133497

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Paul Curtz, Dec 23 2007

EXTENSIONS

Definition clarified by R. J. Mathar, Nov 11 2008

STATUS

approved

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Last modified November 13 12:45 EST 2019. Contains 329094 sequences. (Running on oeis4.)