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 A306595 #23 Mar 06 2019 15:42:14 %S A306595 0,1,1,0,1,2,2,0,1,0,0,3,0,-3,3,0,1,2,2,3,2,3,3,4,2,3,3,4,3,4,4,0,1,0, %T A306595 4,0,0,-9,9,0,4,9,0,8,9,0,8,5,0,0,9,0,-9,-8,0,-5,0,0,8,5,0,-5,5,0,1,2, %U A306595 2,3,2,24,24,4,2,3,3,32,3,4,32,5,2,24,3 %N A306595 Determinant of the circulant matrix whose first column corresponds to the binary digits of n. %C A306595 This sequence is the binary variant of A177894. %C A306595 From _Robert Israel_, Mar 05 2019: (Start) %C A306595 a(n) is divisible by A000120(n). %C A306595 If A070939(n) is even then n is divisible by A000120(n)*A065359(n). (End) %H A306595 Robert Israel, <a href="/A306595/b306595.txt">Table of n, a(n) for n = 0..10000</a> %H A306595 Wikipedia, <a href="https://en.wikipedia.org/wiki/Circulant_matrix">Circulant matrix</a> %H A306595 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a> %F A306595 a(A121016(n)) = 0 for any n > 0. %F A306595 a(2^k) = 1 for any k >= 0. %F A306595 a(A219325(n)) = A219325(n) for any n > 0. %e A306595 For n = 13: %e A306595 - the binary representation of 13 is "1101", %e A306595 - the corresponding circulant matrix is: %e A306595 [1 1 0 1] %e A306595 [1 1 1 0] %e A306595 [0 1 1 1] %e A306595 [1 0 1 1] %e A306595 - its determinant is -3, %e A306595 - hence a(13) = -3. %p A306595 a:= n-> `if`(n=1, 1, (l-> LinearAlgebra[Determinant](Matrix(nops(l), %p A306595 shape=Circulant[l[-i]$i=1..nops(l)])))(convert(n, base, 2))): %p A306595 seq(a(n), n=0..100); # _Alois P. Heinz_, Mar 05 2019 %o A306595 (PARI) a(n) = my (d=if (n, binary(n), [0])); my (m=matrix(#d, #d, i,j, d[1+(i-j)%#d])); return (matdet(m)) %Y A306595 Cf. A000120, A065359, A070939, A121016, A177894, A219325, A306714. %K A306595 sign,base,look %O A306595 0,6 %A A306595 _Rémy Sigrist_, Feb 27 2019