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 A321391 #8 Nov 10 2018 09:55:36 %S A321391 1,1,0,1,1,0,1,2,1,0,1,3,2,1,0,1,4,3,4,1,0,1,5,4,9,4,1,0,1,6,5,16,9,8, %T A321391 1,0,1,7,6,25,16,27,8,1,0,1,8,7,36,25,64,27,16,1,0,1,9,8,49,36,125,64, %U A321391 81,16,1,0,1,10,9,64,49,216,125,256,81,32,1,0 %N A321391 Array read by antidiagonals: T(n,k) is the number of achiral rows of n colors using up to k colors. %C A321391 The antidiagonals go from top-right to bottom-left. %F A321391 T(n,k) = [n==0] + [n>0] * k^ceiling(n/2). %F A321391 The generating function for column k is (1+k*x) / (1-k*x^2). %e A321391 The array begins with T(0,0): %e A321391 1 1 1 1 1 1 1 1 1 1 1 1 ... %e A321391 0 1 2 3 4 5 6 7 8 9 10 11 ... %e A321391 0 1 2 3 4 5 6 7 8 9 10 11 ... %e A321391 0 1 4 9 16 25 36 49 64 81 100 121 ... %e A321391 0 1 4 9 16 25 36 49 64 81 100 121 ... %e A321391 0 1 8 27 64 125 216 343 512 729 1000 1331 ... %e A321391 0 1 8 27 64 125 216 343 512 729 1000 1331 ... %e A321391 0 1 16 81 256 625 1296 2401 4096 6561 10000 14641 ... %e A321391 0 1 16 81 256 625 1296 2401 4096 6561 10000 14641 ... %e A321391 0 1 32 243 1024 3125 7776 16807 32768 59049 100000 161051 ... %e A321391 0 1 32 243 1024 3125 7776 16807 32768 59049 100000 161051 ... %e A321391 0 1 64 729 4096 15625 46656 117649 262144 531441 1000000 1771561 ... %e A321391 For T(3,3)=9, the rows are AAA, ABA, ACA, BAB, BBB, BCB, CAC, CBC, and CCC. %t A321391 Table[If[n>0, (n-k)^Ceiling[k/2], 1], {n, 0, 12}, {k, 0, n}] // Flatten %Y A321391 Columns 0-6 are A000007, A000012, A060546, A056449, A056450, A056451, A056452. %Y A321391 Cf. A003992 (oriented), A277504 (unoriented), A293500 (chiral). %K A321391 nonn,easy,tabl %O A321391 0,8 %A A321391 _Robert A. Russell_, Nov 08 2018