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A191681 a(n) = (9^n - 1)/2. 4
0, 4, 40, 364, 3280, 29524, 265720, 2391484, 21523360, 193710244, 1743392200, 15690529804, 141214768240, 1270932914164, 11438396227480, 102945566047324, 926510094425920, 8338590849833284, 75047317648499560, 675425858836496044 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Number of compositions of odd numbers into n parts < 9.

These are also the junctions of the Collatz trajectories of 2^(2k-1)-1 and 2^2k-1. - David Rabahy, Nov 01 2017

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Adi Dani, Restricted compositions of natural numbers

Index entries for linear recurrences with constant coefficients, signature (10,-9).

FORMULA

a(0)=0, a(1)=4, a(n) = 10*a(n-1) - 9*a(n-2). - Harvey P. Dale, Jun 19 2011

G.f.: 4*x / ((x-1)*(9*x-1)). - Colin Barker, May 16 2013

EXAMPLE

a(2)=40: there are 40 compositions of odd numbers into 2 parts < 9:

1:  (0,1),(1,0);

3:  (0,3),(3,0),(1,2),(2,1);

5:  (0,5),(5,0),(1,4),(4,1),(2,3),(3,2);

7:  (0,7),(7,0),(1,6),(6,1),(2,5),(5,2),(3,4),(4,3);

9:  (1,8),(8,1),(2,7),(7,2),(3,6),(6,3),(4,5),(5,4);

11: (3,8),(8,3),(4,7),(7,4),(5,6),(6,5);

13: (5,8),(8,5),(6,7),(7,6);

15: (7,8),(8,7).

MATHEMATICA

Table[(9^n - 1)/2, {n, 0, 19}]

LinearRecurrence[{10, -9}, {0, 4}, 30] (* Harvey P. Dale, Jun 19 2011 *)

PROG

(MAGMA) [(9^n-1)/2: n in [0..30]]; // Vincenzo Librandi, Jun 16 2011

(PARI) a(n)=9^n\2 \\ Charles R Greathouse IV, Oct 16 2015

CROSSREFS

Cf. A096053, A138894, A198964.

Sequence in context: A069721 A223176 A279574 * A222273 A220366 A220310

Adjacent sequences:  A191678 A191679 A191680 * A191682 A191683 A191684

KEYWORD

nonn,easy

AUTHOR

Adi Dani, Jun 11 2011

EXTENSIONS

Example corrected by L. Edson Jeffery, Feb 13 2015

STATUS

approved

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Last modified June 18 11:24 EDT 2018. Contains 305554 sequences. (Running on oeis4.)