A091159 -id:A091159 - cp's OEIS frontend

A193130 Numbers of spanning trees of the cocktail party graphs.

0, 4, 384, 82944, 32768000, 20736000000, 19271206305792, 24759631762948096, 42071440246337175552, 91403961001574400000000, 247248735803801600000000000, 815050629127324260701847945216, 3217014140995401936351315753959424

Offset: 1

Eric W. Weisstein, Jul 16 2011

Number of trees on 2n labeled vertices containing no edges from a prescribed perfect matching. - Joel B. Lewis, Jun 20 2013

Dragoš M. Cvetković, Michael Doob, Horst Sachs, Spectra of Graphs: Theory and Application, Academic Press, 1980.

Takashi Horiyama, Masahiro Miyasaka, Riku Sasaki, Isomorphism Elimination by Zero-Suppressed Binary Decision Diagrams, 30th Canadian Conference on Computational Geometry, 2018. See Table 2.
Eric Weisstein's World of Mathematics, Cocktail Party Graph
Eric Weisstein's World of Mathematics, Spanning Tree

Cf. A091159 (up to isomorphism).

a(n) = n^(n-2) * (n-1)^n * 4^(n-1). [See "Spectra of graphs", p. 217; also observed by Joel B. Lewis, Jun 20 2013] - Andrey Zabolotskiy, Mar 18 2021

A319587 The number of distinct solid nets of the six convex regular 4D-polytopes in the order of their 3D-cell count.

Original entry on oeis.org

3, 261, 110912, 17895697067018274

Offset: 1

Frank M Jackson, Sep 23 2018

These values have been taken from the Buekenhout (1998) paper (see link). During the unfolding of these solid nets along their common face, the possibility of any overlapping is ignored.

This finite sequence is fully determined but a(5) and a(6) are too large to be displayed in data. See formulas below to calculate these terms.

Andrey Zabolotskiy, Table of n, a(n) for n = 1..6
F. Buekenhout and M. Parker, The number of nets of the regular convex polytopes in dimension >= 4, Discrete Mathematics 186 (1998) 69-94.

Cf. A091159, A201187.

{3, (82944+12*16+24*8+4*2304+6*128+12*96+12*192+12*288)/(2^7*3), 2^5(2^7*3^3+1+3^2), 6(2^19*5688888889+347), 2^7*5^2*7^3(2^114*3^78*5^20*7^33+2^47*3^18*5^2*7^12*53^5*2311^3+239^2*3931^2), 2^188*3^102*5^20*7^36*11^48*23^48*29^30}

a(1) = 3;
a(2) = (82944 + 12*16 + 24*8 + 4*2304 + 6*128 + 12*96 + 12*192 + 12*288)/(2^7 * 3) = 261;
a(3) = 2^5*(2^7 * 3^3 + 1 + 3^2) = 110912;
a(4) = 6*(2^19 * 5688888889 + 347) = 17895697067018274;
a(5) = 2^7 * 5^2 * 7^3 * (2^114 * 3^78 * 5^20 * 7^33 + 2^47 * 3^18 * 5^2 * 7^12 * 53^5 * 2311^3 + 239^2 * 3931^2);
a(6) = 2^188 * 3^102 * 5^20 * 7^36 * 11^48 * 23^48 * 29^30.

cp's OEIS Frontend

A193130 Numbers of spanning trees of the cocktail party graphs.

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