A327372 - OEIS

%I #12 Jan 12 2024 00:50:34

%S 1,0,0,0,0,1,1,0,1,0,3,1,1,1,1,11,5,4,1,2,0,62,29,18,6,4,2,1,510,225,

%T 101,32,13,4,3,0,7459,2674,842,223,72,19,9,3,1,197867,50834,10784,

%U 2171,504,115,34,9,4,0,9808968,1653859,228863,32322,5268,944,209,46,16,4,1

%N Triangle read by rows where T(n,k) is the number of unlabeled simple graphs covering n vertices with exactly k endpoints (vertices of degree 1).

%H Andrew Howroyd, <a href="/A327372/b327372.txt">Table of n, a(n) for n = 0..1325</a> (rows 0..50)

%H Gus Wiseman, <a href="/A327372/a327372.png">The unlabeled graphs covering 5 vertices with k endpoints.</a>

%F Column-wise first differences of A327371.

%e Triangle begins:

%e    1

%e    0  0

%e    0  0  1

%e    1  0  1  0

%e    3  1  1  1  1

%e   11  5  4  1  2  0

%o (PARI) \\ Needs G(n) defined in A327371.

%o T(n)={my(v=Vec(G(n)*(1 - x))); vector(#v, n, Vecrev(v[n], n))}

%o my(A=T(10)); for(n=1, #A, print(A[n])) \\ _Andrew Howroyd_, Jan 11 2024

%Y Row sums are A002494.

%Y Column k = 0 is A261919.

%Y The non-covering version is A327371.

%Y The labeled version is A327377.

%Y Cf. A000088, A004110, A294217, A327227, A327369, A327370.

%K nonn,tabl

%O 0,11

%A _Gus Wiseman_, Sep 04 2019

%E Terms a(21) and beyond from _Andrew Howroyd_, Sep 11 2019