cp's OEIS Frontend

A113114 Triangle T, read by rows, equal to the matrix 5th power of triangle A113106, which satisfies the recurrence: A113106(n,k) = [A113106^5](n-1,k-1) + [A113106^5](n-1,k).

%I A113114 #5 Mar 13 2015 22:32:58
%S A113114 1,5,1,85,30,1,4985,2435,155,1,1082905,662060,61310,780,1,930005021,
%T A113114 671754405,80861810,1528810,3905,1,3306859233805,2718081933706,
%U A113114 399334065655,9987138060,38169435,19530,1,50220281721033905
%N A113114 Triangle T, read by rows, equal to the matrix 5th power of triangle A113106, which satisfies the recurrence: A113106(n,k) = [A113106^5](n-1,k-1) + [A113106^5](n-1,k).
%C A113114 Column 0 equals A113107 shift one place left.
%e A113114 Triangle begins:
%e A113114 1;
%e A113114 5,1;
%e A113114 85,30,1;
%e A113114 4985,2435,155,1;
%e A113114 1082905,662060,61310,780,1;
%e A113114 930005021,671754405,80861810,1528810,3905,1;
%e A113114 3306859233805,2718081933706,399334065655,9987138060,38169435,19530,1;
%o A113114 (PARI) {T(n,k)=local(M=matrix(n+1,n+1));for(r=1,n+1, for(c=1,r, M[r,c]=if(r==c,1,if(c>1,(M^5)[r-1,c-1])+(M^5)[r-1,c]))); return((M^5)[n+1,k+1])}
%Y A113114 Cf. A113106, A113108, A113110, A113112.
%K A113114 nonn,tabl
%O A113114 0,2
%A A113114 _Paul D. Hanna_, Oct 14 2005