cp's OEIS Frontend

A278427 Triangle read by rows: CU(n,k) is the number of unlabeled subgraphs with k edges of the n-cycle C_n.

%I A278427 #24 Sep 27 2019 15:22:48
%S A278427 1,1,1,2,1,1,3,2,1,1,4,3,3,1,1,5,4,5,3,1,1,6,5,7,6,4,1,1,7,6,9,9,8,4,
%T A278427 1,1,8,7,11,12,13,9,5,1,1,9,8,13,15,18,15,12,5,1,1,10,9,15,18,23,22,
%U A278427 21,13,6,1,1,11,10,17,21,28,29,31,24,16,6,1,1
%N A278427 Triangle read by rows: CU(n,k) is the number of unlabeled subgraphs with k edges of the n-cycle C_n.
%H A278427 Andrew Howroyd, <a href="/A278427/b278427.txt">Table of n, a(n) for n = 0..1274</a>
%F A278427 T(n,n) = 1; T(n,k) = Sum_{i=k+1..n} A008284(i, i-k) for k < n. - _Andrew Howroyd_, Sep 26 2019
%e A278427 For row n = 3 of the triangle below: there are 3 unlabeled subgraphs of the triangle C_3 with 0 edges, 2 with 1 edge, 1 with 2 edges, and 1 with 3 edges (C_3 itself).
%e A278427 Triangle begins:
%e A278427    1;
%e A278427    1,  1;
%e A278427    2,  1,  1;
%e A278427    3,  2,  1,  1;
%e A278427    4,  3,  3,  1,  1;
%e A278427    5,  4,  5,  3,  1,  1;
%e A278427    6,  5,  7,  6,  4,  1,  1;
%e A278427    7,  6,  9,  9,  8,  4,  1,  1;
%e A278427    8,  7, 11, 12, 13,  9,  5,  1,  1;
%e A278427    9,  8, 13, 15, 18, 15, 12,  5,  1,  1;
%e A278427   10,  9, 15, 18, 23, 22, 21, 13,  6,  1,  1;
%e A278427   ...
%o A278427 (PARI) \\ here P is A008284 as vector of vectors.
%o A278427 P(n)={[Vecrev(p/y) | p<-Vec(-1 + 1/prod(k=1, n, 1 - y*x^k + O(x*x^n)))]}
%o A278427 T(n)={my(p=P(n-1)); matrix(n, n, n, k, if(k>=n, k==n, sum(i=k, n-1, p[i][i-k+1])))}
%o A278427 { my(A=T(12)); for(n=1, #A, print(A[n,1..n])) } \\ _Andrew Howroyd_, Sep 26 2019
%Y A278427 Cf. A008284.
%Y A278427 Rows sums give A000070.
%Y A278427 Middle diagonal gives A058397.
%K A278427 nonn,tabl
%O A278427 0,4
%A A278427 _John P. McSorley_, Nov 21 2016
%E A278427 Offset corrected and terms a(66) and beyond from _Andrew Howroyd_, Sep 26 2019