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.

A113387 Triangle, read by rows, equal to the matrix cube of A113381.

Original entry on oeis.org

1, 6, 1, 48, 15, 1, 605, 255, 24, 1, 11196, 5630, 624, 33, 1, 280440, 159210, 19484, 1155, 42, 1, 8981460, 5584635, 731664, 46541, 1848, 51, 1, 353283128, 236051661, 32532732, 2173248, 91175, 2703, 60, 1, 16567072675, 11741443007, 1683566556
Offset: 0

Views

Author

Paul D. Hanna, Nov 14 2005

Keywords

Examples

			Triangle A113381^3 begins:
1;
6,1;
48,15,1;
605,255,24,1;
11196,5630,624,33,1;
280440,159210,19484,1155,42,1;
8981460,5584635,731664,46541,1848,51,1;
353283128,236051661,32532732,2173248,91175,2703,60,1;
16567072675,11741443007,1683566556,116647443,5086116,157760,3720,69,1;
		

Crossrefs

Cf. A113381, A113388 (column 0), A113389.

Programs

  • PARI
    T(n,k)=local(A,B);A=Mat(1);for(m=2,n+1,B=matrix(m,m); for(i=1,m, for(j=1,i,if(i<3 || j==i || j>m-1,B[i,j]=1,if(j==1, B[i,1]=1,B[i,j]=(A^(3*j-2))[i-j+1,1]));));A=B); (matrix(#A,#A,r,c,if(r>=c,(A^(3*c-1))[r-c+1,1]))^3)[n+1,k+1]

Formula

Column k of A113381^3 = column 0 of A113389^(3*k+2) for k>=0.

A113392 Triangle, read by rows, equal to the matrix square of triangle A113389. Also given by the matrix product: R^2 = Q^3*(P^-2)*Q, using triangular matrices P=A113370, Q=A113381 and R=A113389.

Original entry on oeis.org

1, 6, 1, 48, 12, 1, 605, 186, 18, 1, 11196, 3892, 414, 24, 1, 280440, 106089, 12021, 732, 30, 1, 8981460, 3620379, 429345, 27152, 1140, 36, 1, 353283128, 149740555, 18386361, 1196910, 51445, 1638, 42, 1, 16567072675, 7316974618, 923656512
Offset: 0

Views

Author

Paul D. Hanna, Nov 14 2005

Keywords

Examples

			Triangle A113389^2 begins:
1;
6,1;
48,12,1;
605,186,18,1;
11196,3892,414,24,1;
280440,106089,12021,732,30,1;
8981460,3620379,429345,27152,1140,36,1;
353283128,149740555,18386361,1196910,51445,1638,42,1;
16567072675,7316974618,923656512,61515702,2696010,87060,2226,48,1;
		

Crossrefs

Cf. A113389, A113388 (column 0), A113393 (column 1).

Programs

  • PARI
    T(n,k)=local(A,B);A=Mat(1);for(m=2,n+1,B=matrix(m,m); for(i=1,m, for(j=1,i,if(i<3 || j==i || j>m-1,B[i,j]=1,if(j==1, B[i,1]=1,B[i,j]=(A^(3*j-2))[i-j+1,1]));));A=B); (matrix(#A,#A,r,c,if(r>=c,(A^(3*c))[r-c+1,1]))^2)[n+1,k+1]

A113393 Column 1 of triangle A113392, also equals column 0 of A113381^6.

Original entry on oeis.org

1, 6, 48, 605, 11196, 280440, 8981460, 353283128, 16567072675, 905357065354, 56632746126107, 3997082539456084, 314584709388906568, 27340439653453247728, 2602372304420672868499, 269388182085308601450047
Offset: 0

Views

Author

Paul D. Hanna, Nov 14 2005

Keywords

Crossrefs

Cf. A113392, A113389, A113381, A113388 (column 0).

Programs

  • PARI
    a(n)=local(A,B);A=Mat(1);for(m=2,n+1,B=matrix(m,m); for(i=1,m, for(j=1,i,if(i<3 || j==i || j>m-1,B[i,j]=1,if(j==1, B[i,1]=1,B[i,j]=(A^(3*j-2))[i-j+1,1]));));A=B); (matrix(#A,#A,r,c,if(r>=c,(A^(3*c))[r-c+1,1]))^2)[n+1,1]

Formula

A113392 equals the matrix square of A113389, which has the property: Column k of A113389^2 = column 0 of A113381^(3*k+3) for k>=0.
Showing 1-3 of 3 results.