A317293 - OEIS

%I #37 Jul 31 2018 09:58:17

%S 1,4,7,11,16,20,28,32,39,46,54,58,72,76,84,96,107,111,126,130,144,156,

%T 164,168,190,199,207,219,235,239

%N 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 Note that in the diagram the number of regions or subparts equals A060831, the partial sums of A001227, n >= 1.

%F a(n) = A317292(n) - A060831(n) + 1 (Euler's formula).

%e Illustration of initial terms (n = 0..9):

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%e .    1    4      7        11         16           20             28

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%e Illustration of the two-dimensional diagram after 29 stages (contains 239 vertices, 300 edges and 62 regions or subparts):

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%e .

%Y For the definition of "subparts" see A279387.

%Y For the triangle of sums of subparts see A279388.

%Y Cf. A317292 (number of edges).

%Y Cf. A060831 (number of regions or subparts).

%Y Compare with A294723 (analog for the diagram that contains only parts).

%Y First differs from A294723 at a(6).

%Y Cf. A000203, A196020, A235791, A237048, A237590, A237591, A237270, A237271, A237593, A245092, A244050, A262626, A280850, A280851, A280940, A285901, A296508, A317109.

%K nonn,more

%O 0,2

%A _Omar E. Pol_, Jul 27 2018