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A290131
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The number of regions in a regular drawing of K_{n,n}.
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2
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0, 2, 12, 40, 96, 204, 368, 634, 1012, 1544, 2236, 3186, 4360, 5898, 7764, 10022, 12712, 16026, 19844, 24448, 29708, 35756, 42604, 50602, 59496, 69650, 80940, 93600, 107540, 123316, 140428, 159642, 180632, 203618, 228556, 255822, 285080, 317326, 352020, 389498
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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LINKS
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Table of n, a(n) for n=1..40.
M. Griffiths, Counting the regions in a regular drawing of K_{n,n}, J. Int. Seq. 13 (2010) # 10.8.5, Table 1.
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FORMULA
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a(n) = A115004(n-1)+(n-1)^2 .
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MAPLE
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A115004 := proc(n)
local a, b, r ;
r := 0 ;
for a from 1 to n do
for b from 1 to n do
if igcd(a, b) = 1 then
r := r+(n+1-a)*(n+1-b);
end if;
end do:
end do:
r ;
end proc:
A290131 := proc(n)
A115004(n-1)+(n-1)^2 ;
end proc:
seq(A290131(n), n=1..30) ;
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PROG
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(Python)
from fractions import gcd
def a115004(n):
r=0
for a in xrange(1, n + 1):
for b in xrange(1, n + 1):
if gcd(a, b)==1:r+=(n + 1 - a)*(n + 1 - b)
return r
def a(n): return a115004(n - 1) + (n - 1)**2
print map(a, xrange(1, 51)) # Indranil Ghosh, Jul 20 2017, after Maple code
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CROSSREFS
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Sequence in context: A086602 A019006 A168057 * A008911 A005719 A143126
Adjacent sequences: A290128 A290129 A290130 * A290132 A290133 A290134
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KEYWORD
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nonn,easy
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AUTHOR
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R. J. Mathar, Jul 20 2017
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STATUS
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approved
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