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 A365608 #23 Feb 16 2025 08:34:06
%S A365608 0,4,100,1060,9316,77092,624484,5019172,40223332,321996580,2576602468,
%T A365608 20614709284,164923342948,1319403749668,10555281015652,84442401180196,
%U A365608 675539668606564,5404318726347556,43234553943265636,345876443943580708,2767011588741012580,22136092821505201444,177088742906772914020
%N A365608 Number of degree 4 vertices in the n-Sierpinski carpet graph.
%C A365608 The level 0 Sierpinski carpet graph is a single vertex. The level n Sierpinski carpet graph is formed from 8 copies of level n-1 by joining boundary vertices between adjacent copies.
%H A365608 Paolo Xausa, <a href="/A365608/b365608.txt">Table of n, a(n) for n = 1..1000</a>
%H A365608 Allan Bickle, <a href="https://allanbickle.files.wordpress.com/2016/05/mengerspongedegree.pdf">Degrees of Menger and Sierpinski Graphs</a>, Congr. Num. 227 (2016) 197-208.
%H A365608 Allan Bickle, <a href="https://allanbickle.files.wordpress.com/2016/05/mengerspongeshort.pdf">MegaMenger Graphs</a>, The College Mathematics Journal, 49 1 (2018) 20-26.
%H A365608 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SierpinskiCarpetGraph.html">Sierpiński Carpet Graph</a>
%H A365608 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (12,-35,24).
%F A365608 a(n) = (3/10)*8^n - (32/15)*3^n + 4.
%F A365608 a(n) = 8*a(n-1) + 32*3^(n-2) - 28.
%F A365608 a(n) = 8^n - A365606(n) - A365607(n).
%F A365608 4*a(n) = 2*A271939(n) - 2*A365606(n) - 3*A365607(n).
%F A365608 G.f.: 4*x^2*(1 + 13*x)/((1 - x)*(1 - 3*x)*(1 - 8*x)). - _Stefano Spezia_, Sep 12 2023
%e A365608 The level 1 Sierpinski carpet graph is an 8-cycle, which has 8 degree 2 vertices and 0 degree 3 or 4 vertices. Thus a(1) = 0.
%t A365608 LinearRecurrence[{12,-35,24},{0,4,100},30] (* _Paolo Xausa_, Oct 16 2023 *)
%o A365608 (Python)
%o A365608 def A365608(n): return ((3<<3*n-1)-(3**(n-1)<<5))//5+4 # _Chai Wah Wu_, Nov 27 2023
%Y A365608 Cf. A001018 (order), A271939 (size).
%Y A365608 Cf. A365606 (degree 2), A365607 (degree 3), A365608 (degree 4).
%Y A365608 Cf. A009964, A291066, A359452, A359453, A291066, A083233, A332705 (Menger sponge graph).
%K A365608 nonn,easy
%O A365608 1,2
%A A365608 _Allan Bickle_, Sep 12 2023