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 A191681 a(n) = (9^n - 1)/2. 7
 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 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 a(n) = 2 * A125857(n+1) = 4 * A002452(n). - Bernard Schott, Oct 29 2021 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. A002452, A096053, A125857, A138894, A198964. Sequence in context: A223176 A279574 A327675 * 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 May 20 01:04 EDT 2022. Contains 353847 sequences. (Running on oeis4.)