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 A317293 #37 Jul 31 2018 09:58:17 %S A317293 1,4,7,11,16,20,28,32,39,46,54,58,72,76,84,96,107,111,126,130,144,156, %T A317293 164,168,190,199,207,219,235,239 %N A317293 a(n) is the total number of vertices after n-th stage in the diagram of the symmetries of sigma in which the parts of width > 1 are dissected into subparts of width 1, with a(0) = 1. %C A317293 Note that in the diagram the number of regions or subparts equals A060831, the partial sums of A001227, n >= 1. %F A317293 a(n) = A317292(n) - A060831(n) + 1 (Euler's formula). %e A317293 Illustration of initial terms (n = 0..9): %e A317293 . _ _ _ _ %e A317293 . _ _ _ |_ _ _ |_ %e A317293 . _ _ _ |_ _ _| |_ _ _| |_|_ %e A317293 . _ _ |_ _ |_ |_ _ |_ _ |_ _ |_ _ | %e A317293 . _ _ |_ _|_ |_ _|_ | |_ _|_ | | |_ _|_ | | | %e A317293 . _ |_ | |_ | | |_ | | | |_ | | | | |_ | | | | | %e A317293 . . |_| |_|_| |_|_|_| |_|_|_|_| |_|_|_|_|_| |_|_|_|_|_|_| %e A317293 . %e A317293 . 1 4 7 11 16 20 28 %e A317293 . %e A317293 . _ _ _ _ _ %e A317293 . _ _ _ _ _ |_ _ _ _ _| %e A317293 . _ _ _ _ |_ _ _ _ | |_ _ _ _ |_ _ %e A317293 . |_ _ _ _| |_ _ _ _| |_ |_ _ _ _| |_ | %e A317293 . |_ _ _ |_ |_ _ _ |_ |_ _ |_ _ _ |_ |_|_ _ %e A317293 . |_ _ _| |_|_ _ |_ _ _| |_|_ _ | |_ _ _| |_|_ _ | | %e A317293 . |_ _ |_ _ | | |_ _ |_ _ | | | |_ _ |_ _ | | | | %e A317293 . |_ _|_ | | | | |_ _|_ | | | | | |_ _|_ | | | | | | %e A317293 . |_ | | | | | | |_ | | | | | | | |_ | | | | | | | | %e A317293 . |_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_| |_|_|_|_|_|_|_|_|_| %e A317293 . %e A317293 . 32 39 46 %e A317293 . %e A317293 . %e A317293 Illustration of the two-dimensional diagram after 29 stages (contains 239 vertices, 300 edges and 62 regions or subparts): %e A317293 ._ _ _ _ _ _ _ _ _ _ _ _ _ _ _ %e A317293 |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _| %e A317293 |_ _ _ _ _ _ _ _ _ _ _ _ _ _ | %e A317293 |_ _ _ _ _ _ _ _ _ _ _ _ _ | | %e A317293 |_ _ _ _ _ _ _ _ _ _ _ _ _| | | %e A317293 |_ _ _ _ _ _ _ _ _ _ _ _ | | |_ _ _ %e A317293 |_ _ _ _ _ _ _ _ _ _ _ _| | |_ _ _ | %e A317293 |_ _ _ _ _ _ _ _ _ _ _ | | |_ _ | |_ %e A317293 |_ _ _ _ _ _ _ _ _ _ _| | |_ _ _| |_ |_ %e A317293 |_ _ _ _ _ _ _ _ _ _ | | |_ _ |_ _| |_|_ %e A317293 |_ _ _ _ _ _ _ _ _ _| | |_ _ | |_ |_ _ |_ _ %e A317293 |_ _ _ _ _ _ _ _ _ | |_ _ _| |_ |_ | |_ _ | %e A317293 |_ _ _ _ _ _ _ _ _| | |_ _ |_ |_ |_|_ _ | | %e A317293 |_ _ _ _ _ _ _ _ | |_ _ |_ _|_ |_ _ | | | |_ _ _ _ _ _ %e A317293 |_ _ _ _ _ _ _ _| | |_ _| |_ | |_ _ | | |_|_ _ _ _ _ | | %e A317293 |_ _ _ _ _ _ _ | |_ _ |_ |_|_ | | |_|_ _ _ _ _ | | | | %e A317293 |_ _ _ _ _ _ _| |_ _ |_ |_ _ | | |_ _ _ _ _ | | | | | | %e A317293 |_ _ _ _ _ _ | |_ |_ |_ | | |_|_ _ _ _ | | | | | | | | %e A317293 |_ _ _ _ _ _| |_ _| |_|_ | |_|_ _ _ _ | | | | | | | | | | %e A317293 |_ _ _ _ _ | |_ |_ _ | |_ _ _ _ | | | | | | | | | | | | %e A317293 |_ _ _ _ _| |_ |_ | |_|_ _ _ | | | | | | | | | | | | | | %e A317293 |_ _ _ _ |_ _|_ |_|_ _ _ | | | | | | | | | | | | | | | | %e A317293 |_ _ _ _| |_ | |_ _ _ | | | | | | | | | | | | | | | | | | %e A317293 |_ _ _ |_ |_|_ _ | | | | | | | | | | | | | | | | | | | | %e A317293 |_ _ _| |_|_ _ | | | | | | | | | | | | | | | | | | | | | | %e A317293 |_ _ |_ _ | | | | | | | | | | | | | | | | | | | | | | | | %e A317293 |_ _|_ | | | | | | | | | | | | | | | | | | | | | | | | | | %e A317293 |_ | | | | | | | | | | | | | | | | | | | | | | | | | | | | %e A317293 |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_| %e A317293 . %Y A317293 For the definition of "subparts" see A279387. %Y A317293 For the triangle of sums of subparts see A279388. %Y A317293 Cf. A317292 (number of edges). %Y A317293 Cf. A060831 (number of regions or subparts). %Y A317293 Compare with A294723 (analog for the diagram that contains only parts). %Y A317293 First differs from A294723 at a(6). %Y A317293 Cf. A000203, A196020, A235791, A237048, A237590, A237591, A237270, A237271, A237593, A245092, A244050, A262626, A280850, A280851, A280940, A285901, A296508, A317109. %K A317293 nonn,more %O A317293 0,2 %A A317293 _Omar E. Pol_, Jul 27 2018