A006237 Complexity of tensor sum of n graphs; or spanning trees on n-cube.

1, 1, 4, 384, 42467328, 20776019874734407680, 1657509127047778993870601546036901052416000000, 153850844349814660487100539994381178281567942393055761257560677644718869248475136000000000000000000000

Offset: 0

Author

N. J. A. Sloane, Don Knuth

Keywords

• nonn
• easy
• nice

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
• R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.6.10.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10
• Aaron R. Bagheri, Classifying the Jacobian Groups of Adinkras, (2017), HMC Senior Theses.
• Frank Harary, John P. Hayes, and Horng-Jyh Wu, A survey of the theory of hypercube graphs, Comput. Math. Appl., 15(4) (1988), 277-289.
• D. E. Knuth, Letter to N. J. A. Sloane, Oct. 1994
• Germain Kreweras, Complexité et circuits Eulériens dans les sommes tensorielles de graphes, J. Combin. Theory, B 24 (1978), 202-212. See p. 210, Parag. 4.
• Eric Weisstein's World of Mathematics, Hypercube Graph
• Eric Weisstein's World of Mathematics, Spanning Tree
• Index entries for sequences related to trees

Crossrefs

Cf. A006235.

Programs

Mathematica

Table[2^(2^n - 1 - n) Product[k^Binomial[n, k], {k, n}], {n, 0, 10}]

PARI

a(n)=2^(2^n-n-1)*prod(k=1,n,k^binomial(n,k))

Formula

a(n) = 2^(2^n-1-n)*1^binomial(n, 1)*2^binomial(n, 2)*...*n^binomial(n, n).

Extensions

Description expanded July 1995