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A102102
Column 0 of triangular matrix A102101, which shifts upward to exclude the main diagonal under matrix fourth power.
1
1, 1, 15, 1000, 189035, 79278446, 63263422646, 86493299281972, 187766975052827491, 611024291011881918991, 2849262494779035461688236, 18362167739517547774072439880, 158759599858376078627687256207242
OFFSET
0,3
COMMENTS
Analogous to A082161 and A082162, this describes the deterministic completely defined initially connected acyclic automata with 4 inputs and n transient unlabeled states (and a unique absorbing state) with a(0)=1.
LINKS
Manosij Ghosh Dastidar and Michael Wallner, Asymptotics of relaxed k-ary trees, arXiv:2404.08415 [math.CO], 2024. See p. 1.4.
PROG
(PARI) {a(n)=local(A=matrix(1, 1), B); A[1, 1]=1; for(m=2, n+1, B=matrix(m, m); for(i=1, m, for(j=1, i, if(j==i, B[i, j]=j, if(j==1, B[i, j]=(A^4)[i-1, 1], B[i, j]=(A^4)[i-1, j])); )); A=B); return(A[n+1, 1])}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Dec 29 2004
STATUS
approved