A113374
Triangle, read by rows, equal to the matrix square of A113370. Also given by the product: P^2 = Q*(R^-2)*Q^3, using triangular matrices P=A113370, Q=A113381 and R=A113389.
Original entry on oeis.org
1, 2, 1, 6, 8, 1, 37, 84, 14, 1, 429, 1296, 252, 20, 1, 7629, 27850, 5957, 510, 26, 1, 185776, 784146, 179270, 16180, 858, 32, 1, 5817106, 27630378, 6641502, 623115, 34125, 1296, 38, 1, 224558216, 1177691946, 294524076, 28470525, 1599091, 61952
Offset: 0
Triangle A113370^2 begins:
1;
2,1;
6,8,1;
37,84,14,1;
429,1296,252,20,1;
7629,27850,5957,510,26,1;
185776,784146,179270,16180,858,32,1;
5817106,27630378,6641502,623115,34125,1296,38,1;
224558216,1177691946,294524076,28470525,1599091,61952,1824,44,1;
-
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);(A^2)[n+1,k+1]
A113375
Column 0 of triangle A113374, also equals column 0 of A113381.
Original entry on oeis.org
1, 2, 6, 37, 429, 7629, 185776, 5817106, 224558216, 10362978307, 558458382528, 34504326965326, 2408502186081117, 187672037804601000, 16162473554575583148, 1525578320627987001344, 156704538246796929248712
Offset: 0
-
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);(A^2)[n+1,1]
A113377
Column 2 of triangle A113374, also equals column 0 of A113381^7.
Original entry on oeis.org
1, 14, 252, 5957, 179270, 6641502, 294524076, 15285260326, 911664081027, 61573228385424, 4652227417900405, 389256081747220268, 35759870451009454561, 3580704593280285017869, 388344720309998846243731
Offset: 0
-
a(n)=local(A,B);A=Mat(1);for(m=2,n+3,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);(A^2)[n+3,3]
Showing 1-3 of 3 results.