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 A038765 #32 Jul 02 2025 16:01:56
%S A038765 1,2,7,24,81,270,891,2916,9477,30618,98415,314928,1003833,3188646,
%T A038765 10097379,31886460,100442349,315675954,990074583,3099363912,
%U A038765 9685512225,30218798142,94143178827,292889889684,910050728661,2824295364810
%N A038765 Next-to-last diagonal of A024462.
%C A038765 If w is a binary string of length 2n-1 and v(w) is a vector of the Hamming weights of each substring of length n, then a(n) is the number of distinct v(w) for all possible w. - _Orson R. L. Peters_, Jun 01 2017
%D A038765 S. J. Cyvin et al., Unbranched catacondensed polygonal systems containing hexagons and tetragons, Croatica Chem. Acta, 69 (1996), 757-774.
%H A038765 Vincenzo Librandi, <a href="/A038765/b038765.txt">Table of n, a(n) for n = 0..1000</a>
%H A038765 Maths.SE, <a href="https://math.stackexchange.com/questions/2302429/number-of-different-counts-of-1s-in-sliding-windows">Number of different counts of 1s in sliding windows</a>.
%H A038765 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-9).
%F A038765 G.f.: (1-2*x)^2/(1-3*x)^2. [Detlef Pauly (dettodet(AT)yahoo.de), Mar 03 2003]
%F A038765 a(n) = 6*a(n-1)-9*a(n-2) for n>2. a(n) = 3^(n-2)*(n+5) for n>0. [_Colin Barker_, Jun 25 2012]
%p A038765 seq(ceil(1/9*3^n*(5+n)),n=0..50);
%t A038765 CoefficientList[Series[(1 - 2 x)^2/(1 - 3 x)^2, {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 22 2013 *)
%t A038765 LinearRecurrence[{6,-9},{1,2,7},30] (* _Harvey P. Dale_, Jul 04 2018 *)
%o A038765 (Magma) [1] cat [3^(n-2)*(n+5): n in [1..30]]; // _Vincenzo Librandi_, Oct 22 2013
%Y A038765 Cf. A024462.
%K A038765 nonn,easy
%O A038765 0,2
%A A038765 _N. J. A. Sloane_, May 03 2000
%E A038765 More terms from _James Sellers_, May 03 2000