cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Views

Author

Paul D. Hanna, May 30 2005

Keywords

Comments

Matrix (2/3)-power of triangle A107717. SHIFT_LEFT of column 0 = 2*(column 1 of A107717). Matrix inverse is A107728.

Examples

			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; ...
		

Crossrefs

Programs

  • PARI
    
    				

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

Views

Author

Paul D. Hanna, May 30 2005

Keywords

Comments

Column 0 is A107720. Column 1 is A107721. Matrix inverse is A107727.

Examples

			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; ...
		

Crossrefs

Programs

  • PARI
    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
    				

A107728 Matrix inverse of A107722.

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

Views

Author

Paul D. Hanna, May 30 2005

Keywords

Comments

Column 0 shift left = -2*A107721, where A107721 = column 1 of A107719. Column 1 shift left = 2*(column 0) shift left. Matrix square of A107727.

Examples

			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; ...
		

Crossrefs

Programs

  • PARI
    {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.