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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). 1

%I #5 Mar 13 2015 22:32:58

%S 1,5,1,85,30,1,4985,2435,155,1,1082905,662060,61310,780,1,930005021,

%T 671754405,80861810,1528810,3905,1,3306859233805,2718081933706,

%U 399334065655,9987138060,38169435,19530,1,50220281721033905

%N 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 Column 0 equals A113107 shift one place left.

%e Triangle begins:

%e 1;

%e 5,1;

%e 85,30,1;

%e 4985,2435,155,1;

%e 1082905,662060,61310,780,1;

%e 930005021,671754405,80861810,1528810,3905,1;

%e 3306859233805,2718081933706,399334065655,9987138060,38169435,19530,1;

%o (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 Cf. A113106, A113108, A113110, A113112.

%K nonn,tabl

%O 0,2

%A _Paul D. Hanna_, Oct 14 2005

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)