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A212798
Row 3 of array in A212796.
4
3, 294, 11664, 367500, 10609215, 292626432, 7839321861, 205683135000, 5312031978672, 135495143785470, 3421536337406913, 85686871818240000, 2130987634616000199, 52682956706683197258, 1295799745309605101520, 31730077997731715070000
OFFSET
1,1
COMMENTS
A linear divisibility sequence of order 10. - Peter Bala, May 04 2014
LINKS
Germain Kreweras, Complexite et circuits Euleriens 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 (58,-1131,8700,-29493,43734,-29493,8700,-1131,58,-1).
FORMULA
From Peter Bala, May 04 2014: (Start)
a(n) = n/3*(-2 + ( (5 + sqrt(21))/2 )^n + ( (5 - sqrt(21))/2 )^n)^2 = 3*n*A054493(n-1)^2.
O.g.f.: 3*(x^8 + 40*x^7 - 665*x^6 - 866*x^5 + 5626*x^4 - 866*x^3 - 665*x^2 + 40*x + 1)/( (x - 1)^2*(x^2 - 5*x + 1)^2*(x^2 - 23*x + 1)^2 ). (End)
MAPLE
seq(simplify(n/3*(-2 + ( (5 + sqrt(21))/2 )^n + ( (5 - sqrt(21))/2 )^n)^2), n = 1..14); # Peter Bala, May 04 2014
PROG
(Python)
# Using graphillion
from graphillion import GraphSet
def make_CnXCk(n, k):
grids = []
for i in range(1, k + 1):
for j in range(1, n):
grids.append((i + (j - 1) * k, i + j * k))
grids.append((i + (n - 1) * k, i))
for i in range(1, k * n, k):
for j in range(1, k):
grids.append((i + j - 1, i + j))
grids.append((i + k - 1, i))
return grids
def A212798(n):
if n == 1: return 3
if n == 2: return 294
universe = make_CnXCk(n, 3)
GraphSet.set_universe(universe)
spanning_trees = GraphSet.trees(is_spanning=True)
return spanning_trees.len()
print([A212798(n) for n in range(1, 30)]) # Seiichi Manyama, Nov 22 2020
CROSSREFS
Sequence in context: A199644 A347138 A124357 * A157579 A104821 A282195
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, May 27 2012
EXTENSIONS
More terms from Peter Bala, May 04 2014
STATUS
approved