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A290132
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The number of edges in a graph induced by a regular drawing of K_{n,n}.
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6
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1, 6, 24, 74, 170, 362, 642, 1110, 1766, 2706, 3894, 5558, 7602, 10326, 13562, 17510, 22178, 28006, 34634, 42722, 51922, 62570, 74450, 88462, 103994, 121862, 141482, 163610, 187886, 215578, 245430, 279198, 315958, 356390, 399830, 447542, 498626, 555278, 615698, 681206
(list;
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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FORMULA
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MAPLE
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end proc:
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MATHEMATICA
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b[n_] := Sum[(n-i+1)(n-j+1) Boole[GCD[i, j] == 1], {i, n}, {j, n}];
A159065[n_] := Module[{x, y, s1 = 0, s2 = 0}, For[x = 1, x <= n - 1, x++, For[y = 1, y <= n - 1, y++, If[GCD[x, y] == 1, s1 += (n - x)(n - y); If[2x <= n - 1 && 2y <= n - 1, s2 += (n - 2x)(n - 2y)]]]]; s1 - s2];
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PROG
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(Python)
from math import gcd
def a115004(n):
r=0
for a in range(1, n + 1):
for b in range(1, n + 1):
if gcd(a, b)==1:r+=(n + 1 - a)*(n + 1 - b)
return r
def a159065(n):
c=0
for a in range(1, n):
for b in range(1, n):
if gcd(a, b)==1:
c+=(n - a)*(n - b)
if 2*a<n and 2*b<n:c-=(n - 2*a)*(n - 2*b)
return c
def a290131(n): return a115004(n - 1) + (n - 1)**2
def a(n): return 2*n + a290131(n) + a159065(n) - 1
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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