A182043 Table, by rows, of T(k,n) the number of simple graphs on v = prime(n) vertices and with e = prime(k) edges.

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

Author

Jonathan Vos Post, Apr 07 2012

Keywords

• nonn
• tabf

Examples

			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 |
  +---+---+---+---+---+
		

Links

• Eric Weisstein's World of Mathematics, Simple Graph.

Crossrefs

Cf. A008406.

Programs

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

Extensions

Terms from row 4 on by R. J. Mathar, Oct 20 2013