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
a(n) gives the number of turns in the n-th iteration of the Peano curve given by plotting (A163528, A163529) or by (Siromoney 1982). - Jason V. Morgan, Oct 08 2021
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Rani Siromoney and K. G. Subramanian, Space-filling curves and infinite graphs, International Workshop on Graph Grammars and Their Application to Computer Science, 1982.
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
KEYWORD
nonn,easy
AUTHOR
Adi Dani, Jun 11 2011
EXTENSIONS
Example corrected by L. Edson Jeffery, Feb 13 2015
STATUS
approved