A107722
Matrix square of triangle A107721, read by rows.
Original entry on oeis.org
1, 2, 1, 12, 4, 1, 114, 32, 6, 1, 1446, 364, 62, 8, 1, 22722, 5276, 854, 102, 10, 1, 424302, 92332, 14466, 1664, 152, 12, 1, 9168162, 1889012, 289222, 32536, 2874, 212, 14, 1, 224961774, 44207212, 6652522, 737472, 63886, 4564, 282, 16, 1, 6180211842
Offset: 0
Triangle begins:
1;
2,1;
12,4,1;
114,32,6,1;
1446,364,62,8,1;
22722,5276,854,102,10,1;
424302,92332,14466,1664,152,12,1;
9168162,1889012,289222,32536,2874,212,14,1; ...
A107719
Matrix cube-root of triangle A107717.
Original entry on oeis.org
1, 1, 1, 5, 2, 1, 43, 13, 3, 1, 509, 131, 25, 4, 1, 7579, 1741, 303, 41, 5, 1, 135341, 28451, 4681, 587, 61, 6, 1, 2813851, 549757, 87039, 10449, 1011, 85, 7, 1, 66733853, 12247211, 1885177, 220023, 20445, 1603, 113, 8, 1, 1778159275, 308953453
Offset: 0
Triangle begins:
1;
1,1;
5,2,1;
43,13,3,1;
509,131,25,4,1;
7579,1741,303,41,5,1;
135341,28451,4681,587,61,6,1;
2813851,549757,87039,10449,1011,85,7,1; ...
-
T(n,k)=local(E,L,M=matrix(n+1,n+1,m,j,if(m>=j,if(m==j,1,if(m==j+1,-3*j, -polcoeff(1-(1+sum(c=1,m-j,prod(i=0,c-1,3*i+1)*x^c)+x*O(x^(m-j)))^-1,m-j);))))^-1); L=matrix(#M,#M,r,c,if(r>=c,sum(i=1,#M,(-1)^(i-1)*(M-M^0)^i/i)[r,c])); E=matrix(#L,#L,r,c,if(r>=c,sum(i=0,#L,L^i/3^i/i!)[r,c])); if(n
Original entry on oeis.org
1, -2, 1, -4, -4, 1, -26, -8, -6, 1, -262, -52, -14, -8, 1, -3482, -524, -102, -22, -10, 1, -56902, -6964, -1130, -184, -32, -12, 1, -1099514, -113804, -16326, -2304, -306, -44, -14, 1, -24494422, -2199028, -287882, -37224, -4326, -476, -58, -16, 1, -617906906, -48988844, -5969382, -727928, -78114
Offset: 0
Triangle begins:
1;
-2,1;
-4,-4,1;
-26,-8,-6,1;
-262,-52,-14,-8,1;
-3482,-524,-102,-22,-10,1;
-56902,-6964,-1130,-184,-32,-12,1;
-1099514,-113804,-16326,-2304,-306,-44,-14,1; ...
-
{T(n,k)=local(L,N,M=matrix(n+1,n+1,m,j,if(m>=j,if(m==j,1,if(m==j+1,-3*j, polcoeff(1/sum(i=0,m-j,prod(r=0,i-1,3*r+1)*x^i)+O(x^m),m-j)))))^-1); L=sum(i=1,#M,(M^0-M)^i/i)/3;N=sum(i=0,#L,L^i/i!); return(if(n<0,0,(N^2)[n+1,k+1]))}
Showing 1-3 of 3 results.
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