A001930 -id:A001930 - cp's OEIS frontend

A101620 Decimal encoding of digraph topologies.

1, 3, 9, 11, 13, 15, 129, 131, 133, 137, 139, 141, 143, 145, 153, 161, 163, 165, 171, 175, 177, 179, 187, 193, 195, 197, 205, 207, 209, 213, 221, 241, 243, 245, 255

Offset: 1

Alford Arnold, Dec 10 2004

The sequence encodes labeled digraph topologies as described by and counted in A000798.

			Let a = 2, b = 4, c = 16, d = 256, ...
a(19) = 171 because we can map { }, a, ab, ac, abc to 1 + 2 + 8 + 32 + 128
Viewed as an array the table begins
1
3
9 11 13 15
129 131 133 137 139 141 143 145 153 161 163 165 171 175 177 ...
with respectively 1 1 4 29 355 ... (A000798) entries on each row.

Cf. A000798, A001035, A001930, A074486.

A173399 Partial sums of A000798.

Original entry on oeis.org

1, 2, 6, 35, 390, 7332, 216859, 9752100, 652531454, 63912820877, 9040966693920, 1825887005430112, 521181458071204133, 208402575114740157174, 115825454552169007964634, 88852094573138413500449755, 93499965506283177978710943850, 134231450058844163850300579669696, 261626767193693218968916427480786899

Offset: 0

Jonathan Vos Post, Feb 17 2010

nonn

Number of different quasi-orders (or topologies, or transitive digraphs) with n labeled elements.

The subsequence of primes in this partial sum begins: 2, 216859.

Cf. A000798, A001035 (labeled posets), A001930 (unlabeled topologies), A000112 (unlabeled posets), A006057.

Cases[Import["https://oeis.org/A000798/b000798.txt", "Table"], {, }][[All, 2]] // Accumulate (* Jean-François Alcover, Dec 30 2019 *)

a(n) = Sum_{i=0..n} A000798(i).

Missing term 7332 added and extended by Jean-François Alcover, Dec 30 2019

cp's OEIS Frontend

A101620 Decimal encoding of digraph topologies.

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A173399 Partial sums of A000798.

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