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A191681 a(n) = (9^n - 1)/2. 4

%I

%S 0,4,40,364,3280,29524,265720,2391484,21523360,193710244,1743392200,

%T 15690529804,141214768240,1270932914164,11438396227480,

%U 102945566047324,926510094425920,8338590849833284,75047317648499560,675425858836496044

%N a(n) = (9^n - 1)/2.

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

%C These are also the junctions of the Collatz trajectories of 2^(2k-1)-1 and 2^2k-1. - _David Rabahy_, Nov 01 2017

%H Vincenzo Librandi, <a href="/A191681/b191681.txt">Table of n, a(n) for n = 0..200</a>

%H Adi Dani, <a href="https://oeis.org/wiki/User:Adi_Dani_/Restricted_compositions_of_natural_numbers">Restricted compositions of natural numbers</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-9).

%F a(0)=0, a(1)=4, a(n) = 10*a(n-1) - 9*a(n-2). - _Harvey P. Dale_, Jun 19 2011

%F G.f.: 4*x / ((x-1)*(9*x-1)). - _Colin Barker_, May 16 2013

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

%e 1: (0,1),(1,0);

%e 3: (0,3),(3,0),(1,2),(2,1);

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

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

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

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

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

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

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

%t LinearRecurrence[{10,-9},{0,4},30] (* _Harvey P. Dale_, Jun 19 2011 *)

%o (MAGMA) [(9^n-1)/2: n in [0..30]]; // _Vincenzo Librandi_, Jun 16 2011

%o (PARI) a(n)=9^n\2 \\ _Charles R Greathouse IV_, Oct 16 2015

%Y Cf. A096053, A138894, A198964.

%K nonn,easy

%O 0,2

%A _Adi Dani_, Jun 11 2011

%E Example corrected by _L. Edson Jeffery_, Feb 13 2015

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Last modified October 23 03:21 EDT 2019. Contains 328335 sequences. (Running on oeis4.)