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 A361398 #17 Mar 15 2023 16:27:38 %S A361398 1,2,5,3,9,12,9,4,14,28,30,21,19,21,14,5,20,53,68,60,55,74,68,32,34, %T A361398 60,55,36,34,32,20,6,27,89,126,134,120,181,196,108,88,181,183,136,151, %U A361398 164,126,45,55,134,151,129,107,136,120,54,69,108,88,54,55,45,27 %N A361398 An infiltration of two words, say x and y, is a shuffle of x and y optionally followed by replacements of pairs of consecutive equal symbols, say two d's, one of which comes from x and the other from y, by a single d (that cannot be part of another replacement); a(n) is the number of distinct infiltrations of the word given by the binary representation of n with itself. %C A361398 Leading zeros in binary expansions are ignored. %C A361398 See A191755 for the definition of a shuffle. %H A361398 Rémy Sigrist, <a href="/A361398/b361398.txt">Table of n, a(n) for n = 0..8192</a> %H A361398 Rémy Sigrist, <a href="/A361398/a361398.gp.txt">PARI program</a> %H A361398 Wikipedia, <a href="https://en.wikipedia.org/wiki/Shuffle_algebra#Infiltration_product">Infiltration product</a>. %H A361398 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a> %F A361398 a(n) >= A193020(n). %F A361398 a(2^k - 1) = k + 1 for any k >= 0. %F A361398 a(2^k) = A000096(k + 1) for any k >= 0. %e A361398 For n = 2: %e A361398 - the binary expansion of 2 is "10", %e A361398 - we have essentially the following infiltrations: %e A361398 x 10 10 1 0 10 1 0 %e A361398 y 10 1 0 10 10 1 0 %e A361398 -- --- --- ---- ---- %e A361398 infiltration 10 100 110 1010 1100 %e A361398 - so a(2) = 5. %o A361398 (PARI) See Links section. %Y A361398 Cf. A000096, A191755, A193020. %K A361398 nonn,base %O A361398 0,2 %A A361398 _Rémy Sigrist_, Mar 10 2023