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 A125831 #67 Dec 15 2023 09:10:43
%S A125831 0,2,12,62,312,1562,7812,39062,195312,976562,4882812,24414062,
%T A125831 122070312,610351562,3051757812,15258789062,76293945312,381469726562,
%U A125831 1907348632812,9536743164062,47683715820312,238418579101562,1192092895507812,5960464477539062,29802322387695312
%N A125831 a(n) = (5^n - 1)/2.
%C A125831 Number of compositions of odd numbers into n parts < 5. - _Adi Dani_, Jun 11 2011
%C A125831 Numbers whose base 5 representation is 22222...2 (n times).
%D A125831 S. J. Cyvin, B. N. Cyvin, and J. Brunvoll. Enumeration of tree-like octagonal systems: catapolyoctagons, ACH Models in Chem. 134 (1997), pp. 55-70, eqs. (6) and (7) on p. 58.
%H A125831 Vincenzo Librandi, <a href="/A125831/b125831.txt">Table of n, a(n) for n = 0..300</a>
%H A125831 Adi Dani, <a href="https://oeis.org/wiki/User:Adi_Dani_/Restricted_compositions_of_natural_numbers">Restricted compositions of natural numbers</a>.
%H A125831 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-5).
%F A125831 a(n) = 5*a(n-1) + 2 for n > 0, a(0)=0. - _Vincenzo Librandi_, Sep 30 2010
%F A125831 From _Colin Barker_, May 16 2013: (Start)
%F A125831 a(n) = 6*a(n-1) - 5*a(n-2).
%F A125831 G.f.: 2*x/((1-x)*(1-5*x)). (End)
%F A125831 a(n) = 2*A003463(n). - _Joerg Arndt_, Aug 03 2019
%F A125831 From _Elmo R. Oliveira_, Dec 10 2023: (Start)
%F A125831 a(n) = A024049(n)/2.
%F A125831 E.g.f.: (1/2)*(exp(5*x) - exp(x)). (End)
%e A125831 a(2)=12: there are 12 compositions of odd numbers into 2 parts < 5:
%e A125831 1: (0,1),(1,0);
%e A125831 3: (0,3),(3,0),(1,2),(2,1);
%e A125831 5: (1,4),(4,1),(2,3),(3,2);
%e A125831 7: (3,4),(4,3). - _Adi Dani_, Jun 11 2011
%p A125831 seq((5^n-1)/2, n=0..30);
%t A125831 Table[(5^n -1)/2, {n, 0, 30}] (* _Harvey P. Dale_, Dec 03 2010 *)
%o A125831 (Magma) [(5^n-1)/2: n in [0..30]]; // _Vincenzo Librandi_, Jun 11 2011
%o A125831 (PARI) a(n)=5^n\2 \\ _Charles R Greathouse IV_, Jun 11 2011
%o A125831 (Sage) [(5^n-1)/2 for n in (0..30)] # _G. C. Greubel_, Aug 03 2019
%o A125831 (GAP) List([0..30], n-> (5^n-1)/2); # _G. C. Greubel_, Aug 03 2019
%Y A125831 Cf. A003463, A024049, A121177 (same with different offset).
%K A125831 easy,nonn
%O A125831 0,2
%A A125831 _Zerinvary Lajos_, Feb 03 2007
%E A125831 Offset corrected by _N. J. A. Sloane_, Oct 02 2010
%E A125831 Major edit by _Joerg Arndt_, Jun 11 2011