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A182043
Table, by rows, of T(k,n) the number of simple graphs on v = prime(n) vertices and with e = prime(k) edges.
0
1, 1, 2, 4, 6, 4, 2, 5, 21, 65, 148, 97, 10, 2, 2, 5, 26, 172, 10250, 75415, 2295898, 8640134, 53037356, 99187806, 70065437, 4609179, 192788, 28259, 467, 2, 2, 5, 26, 176, 14140, 154658, 17422984, 152339952, 6461056816, 359954668522, 899632282299, 4093273437761, 4093273437761
OFFSET
2,3
LINKS
Eric Weisstein's World of Mathematics, Simple Graph.
EXAMPLE
T(3,4) = 4 because there are 4 simple graphs with prime(3) = 5 vertices and prime(4) = 7 edges.
The table begins:
+---+---+---+---+
|e=2|e=3|e=5|e=7|
+---+---+---+---+---+
|v=3| 1 | 1 | | |
+---+---+---+---+---+
|v=5| 2 | 4 | 6 | 4 |
+---+---+---+---+---+
MAPLE
read("transforms3") :
L := BFILETOLIST("b008406.txt") ;
A008406 := proc(n, k)
global L ;
local f, r ;
f := 1 ;
r := 1 ;
while r < n do
f := f+r*(r-1)/2+1 ;
r := r+1 ;
end do:
op(f+k, L) ;
end proc:
for n from 1 do
v := ithprime(n) ;
for k from 1 do
e := ithprime(k) ;
if e > v*(v-1)/2 then
break;
else
printf("%d, ", A008406(v, e)) ;
end if;
end do:
end do: # R. J. Mathar, Oct 20 2013
CROSSREFS
Cf. A008406.
Sequence in context: A317310 A231655 A018841 * A337937 A138125 A098793
KEYWORD
nonn,tabf
AUTHOR
Jonathan Vos Post, Apr 07 2012
EXTENSIONS
Terms from row 4 on by R. J. Mathar, Oct 20 2013
STATUS
approved