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A212799
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Row 4 of array in A212796.
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2
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4, 2304, 367500, 42467328, 4381392020, 428652000000, 40643137651228, 3771854305099776, 344499209234302500, 31074298464967845120, 2774871814779003772844, 245741556726521856000000, 21611621448116558812137652, 1889376666754339457990201088, 164334311374716912516773437500
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) ~ (21 + 12*sqrt(3) + 2*sqrt(2*(97 + 56*sqrt(3))))^n * n/4.
G.f.: 4*x*(1 + 310*x - 33278*x^2 + 785814*x^3 + 4923451*x^4 - 476492324*x^5 + 8394222196*x^6 - 74272031652*x^7 + 371582629705*x^8 - 981246223862*x^9 + 441533151262*x^10 + 6161037199338*x^11 - 23802532730757*x^12 + 46995963516168*x^13 - 58240430817576*x^14 + 46995963516168*x^15 - 23802532730757*x^16 + 6161037199338*x^17 + 441533151262*x^18 - 981246223862*x^19 + 371582629705*x^20 - 74272031652*x^21 + 8394222196*x^22 - 476492324*x^23 + 4923451*x^24 + 785814*x^25 - 33278*x^26 + 310*x^27 + x^28)/ ((1 - x)^2*(1 - 14*x + x^2)^2*(1 - 6*x + x^2)^2*(1 - 4*x + x^2)^2* (1 - 84*x + 230*x^2 - 84*x^3 + x^4)^2*(1 - 24*x + 50*x^2 - 24*x^3 + x^4)^2). (End)
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MATHEMATICA
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Table[2^(6*n-4)*n*Product[Sin[j*Pi/4]^2 + Sin[k*Pi/n]^2, {j, 1, 3}, {k, 1, n-1}], {n, 1, 20}]//Round (* Vaclav Kotesovec, Feb 26 2021 *)
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PROG
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(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
if n == 1: return 4
if n == 2: return 2304
universe = make_CnXCk(4, n)
GraphSet.set_universe(universe)
spanning_trees = GraphSet.trees(is_spanning=True)
return spanning_trees.len()
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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