A232967 Irregular triangle read by rows: row n lists the rank sizes of the "electrical" poset EP_n of circular planar graphs with n boundary vertices.

1, 1, 1, 1, 3, 3, 1, 1, 6, 14, 16, 10, 4, 1, 1, 10, 40, 85, 110, 97, 65, 35, 15, 5, 1, 1, 15, 90, 295, 609, 873, 948, 840, 636, 421, 246, 126, 56, 21, 6, 1, 1, 21, 175, 805, 2366, 4872, 7567, 9459, 10031, 9359, 7861, 6027, 4249, 2765, 1661, 917, 462, 210, 84, 28, 7, 1, 1, 28, 308, 1876, 7350, 20272, 42090, 69620, 96334, 115980, 125044, 123176, 112380, 95836, 76868, 58220, 41734, 28344, 18236, 11096, 6364, 3424, 1716, 792, 330, 120, 36, 8, 1

Offset

1,5

Comments

More than the usual number of terms are given, since the connection with A111088 seems rather mysterious.

Links

Table of n, a(n) for n=1..92.

J. Alman, C. Lian, and B. Tran, Circular Planar Electrical Networks: Posets and Positivity, 2013.

Example

Triangle begins:
1,
1, 1,
1, 3, 3, 1,
1, 6, 14, 16, 10, 4, 1,
1, 10, 40, 85, 110, 97, 65, 35, 15, 5, 1,,
1, 15, 90, 295, 609, 873, 948, 840, 636, 421, 246, 126, 56, 21, 6, 1,
1, 21, 175, 805, 2366, 4872, 7567, 9459, 10031, 9359, 7861, 6027, 4249, 2765, 1661, 917, 462, 210, 84, 28, 7, 1,
1, 28, 308, 1876, 7350, 20272, 42090, 69620, 96334, 115980, 125044, 123176, 112380, 95836, 76868, 58220, 41734, 28344, 18236, 11096, 6364, 3424, 1716, 792, 330, 120, 36, 8, 1,
...

Crossrefs

Row sums give A111088.

Sequence in context: A244500 A300695 A296186 * A144163 A352472 A080858

Adjacent sequences: A232964 A232965 A232966 * A232968 A232969 A232970

Keyword

nonn,tabf

Author

N. J. A. Sloane, Dec 04 2013

Status

approved