This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A191681 #61 Sep 08 2022 08:45:57
%S A191681 0,4,40,364,3280,29524,265720,2391484,21523360,193710244,1743392200,
%T A191681 15690529804,141214768240,1270932914164,11438396227480,
%U A191681 102945566047324,926510094425920,8338590849833284,75047317648499560,675425858836496044
%N A191681 a(n) = (9^n - 1)/2.
%C A191681 Number of compositions of odd numbers into n parts < 9.
%C A191681 These are also the junctions of the Collatz trajectories of 2^(2k-1)-1 and 2^2k-1. - _David Rabahy_, Nov 01 2017
%C A191681 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
%H A191681 Vincenzo Librandi, <a href="/A191681/b191681.txt">Table of n, a(n) for n = 0..200</a>
%H A191681 Adi Dani, <a href="https://oeis.org/wiki/User:Adi_Dani_/Restricted_compositions_of_natural_numbers">Restricted compositions of natural numbers</a>
%H A191681 Rani Siromoney and K. G. Subramanian, <a href="https://doi.org/10.1007/BFb0000120">Space-filling curves and infinite graphs</a>, International Workshop on Graph Grammars and Their Application to Computer Science, 1982.
%H A191681 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-9).
%F A191681 a(0)=0, a(1)=4, a(n) = 10*a(n-1) - 9*a(n-2). - _Harvey P. Dale_, Jun 19 2011
%F A191681 G.f.: 4*x / ((x-1)*(9*x-1)). - _Colin Barker_, May 16 2013
%F A191681 a(n) = 2 * A125857(n+1) = 4 * A002452(n). - _Bernard Schott_, Oct 29 2021
%e A191681 a(2)=40: there are 40 compositions of odd numbers into 2 parts < 9:
%e A191681 1: (0,1),(1,0);
%e A191681 3: (0,3),(3,0),(1,2),(2,1);
%e A191681 5: (0,5),(5,0),(1,4),(4,1),(2,3),(3,2);
%e A191681 7: (0,7),(7,0),(1,6),(6,1),(2,5),(5,2),(3,4),(4,3);
%e A191681 9: (1,8),(8,1),(2,7),(7,2),(3,6),(6,3),(4,5),(5,4);
%e A191681 11: (3,8),(8,3),(4,7),(7,4),(5,6),(6,5);
%e A191681 13: (5,8),(8,5),(6,7),(7,6);
%e A191681 15: (7,8),(8,7).
%t A191681 Table[(9^n - 1)/2, {n, 0, 19}]
%t A191681 LinearRecurrence[{10,-9},{0,4},30] (* _Harvey P. Dale_, Jun 19 2011 *)
%o A191681 (Magma) [(9^n-1)/2: n in [0..30]]; // _Vincenzo Librandi_, Jun 16 2011
%o A191681 (PARI) a(n)=9^n\2 \\ _Charles R Greathouse IV_, Oct 16 2015
%Y A191681 Cf. A002452, A096053, A125857, A138894, A198964.
%K A191681 nonn,easy
%O A191681 0,2
%A A191681 _Adi Dani_, Jun 11 2011
%E A191681 Example corrected by _L. Edson Jeffery_, Feb 13 2015