A212797 Number of spanning trees in C_2 X C_n.

2, 32, 294, 2304, 16810, 117600, 799694, 5326848, 34928082, 226195360, 1450199542, 9220780800, 58221203066, 365440965344, 2282085037470, 14187697422336, 87860208024994, 542209573735200, 3335797263902918, 20465738163774720, 125247216613782858

Offset: 1

Author

N. J. A. Sloane, May 27 2012

Keywords

• nonn

Comments

From Harry Richman and Alois P. Heinz, Jan 31 2023: (Start)

Row 2 of array in A212796.

a(n) is a divisibility sequence, i.e., if m divides n then a(m) divides a(n), since A001108 is one. (End)

Links

• 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.
• Index entries for linear recurrences with constant coefficients, signature (14,-63,100,-63,14,-1).

Crossrefs

Cf. A001108, A212796.

Programs

PARI

default(realprecision, 120);
{a(n) = round(n*2^(2*n-1)*prod(k=1, n-1, 1+sin(k*Pi/n)^2))} \\ Seiichi Manyama, Jan 13 2021

PARI

my(N=66, x='x+O('x^N)); Vec(2*x*deriv(x*(1+x)/((1-x)*(1-6*x+x^2)))) \\ Seiichi Manyama, Jan 13 2021

Formula

G.f.: 2*x*(1+2*x-14*x^2+2*x^3+x^4)/((x-1)^2*(1-6*x+x^2)^2) . - R. J. Mathar, Apr 16 2018

Conjecture: a(n) = 16*A001109(n+1) +3*A001109(n) -16*(A144133(n)-6*A144133(n-1)) -n = 3*A144133(n-1) -2*A144133(n-2) +3*A144133(n-3) -n. - R. J. Mathar, Apr 16 2018

From Seiichi Manyama, Jan 13 2021: (Start)

a(n) = 2 * n * A001108(n).

a(n) = 14*a(n-1) - 63*a(n-2) + 100*a(n-3) - 63*a(n-4) + 14*a(n-5) - a(n-6) for n > 6. (End)

Extensions

More terms from Seiichi Manyama, Jan 13 2021