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

Author

N. J. A. Sloane, Dec 04 2013

Keywords

• nonn
• tabf

Comments

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

Examples

			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,
...
		

Links

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

Crossrefs

Row sums give A111088.