A113355
Triangle T, read by rows, equal to the matrix square of triangle A113350, where T transforms column k of T into column k+1 of T.
Original entry on oeis.org
1, 4, 1, 18, 8, 1, 112, 68, 12, 1, 965, 712, 150, 16, 1, 10957, 9270, 2184, 264, 20, 1, 156699, 147174, 37523, 4912, 410, 24, 1, 2727793, 2786270, 754171, 104476, 9280, 588, 28, 1, 56306695, 61662544, 17502145, 2531004, 235025, 15672, 798, 32, 1
Offset: 0
Triangle T begins:
1;
4,1;
18,8,1;
112,68,12,1;
965,712,150,16,1;
10957,9270,2184,264,20,1;
156699,147174,37523,4912,410,24,1;
2727793,2786270,754171,104476,9280,588,28,1;
56306695,61662544,17502145,2531004,235025,15672,798,32,1; ...
where T transforms column k of T into column k+1:
at k=0, [Q^2]*[1,4,18,112,965,...] = [1,8,68,712,9270,...];
at k=1, [Q^2]*[1,8,68,712,9270,...] = [1,12,150,2184,37523,...].
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T(n,k)=local(A,B);A=matrix(1,1);A[1,1]=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^(2*j-1))[i-j+1,1]));));A=B); (matrix(#A,#A,r,c,if(r>=c,(A^(2*c))[r-c+1,1]))^2)[n+1,k+1]
A113356
Column 0 of triangle A113355, which is the matrix square of A113350.
Original entry on oeis.org
1, 4, 18, 112, 965, 10957, 156699, 2727793, 56306695, 1350043964, 36979531548, 1141573025171, 39272377323692, 1491452150268435, 62027842189908230, 2805631215820328991, 137199563717151509076, 7215932308408758314446
Offset: 0
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a(n)=local(A,B);A=matrix(1,1);A[1,1]=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^(2*j-1))[i-j+1,1]));));A=B); (matrix(#A,#A,r,c,if(r>=c,(A^(2*c))[r-c+1,1]))^2)[n+1,1]
A113358
Column 2 of triangle A113355, also equals column 0 of A113355^3.
Original entry on oeis.org
1, 12, 150, 2184, 37523, 754171, 17502145, 462930509, 13792292332, 458112945183, 16812390472566, 676432435584855, 29635374525536866, 1405425902409792025, 71770681806834337871, 3928431507732054301085, 229528875492540329214765
Offset: 0
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a(n)=local(A,B);A=matrix(1,1);A[1,1]=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^(2*j-1))[i-j+1,1]));));A=B); (matrix(#A,#A,r,c,if(r>=c,(A^(2*c))[r-c+1,1]))^2)[n+3,3]
A113359
Column 3 of triangle A113355, also equals column 0 of A113355^4.
Original entry on oeis.org
1, 16, 264, 4912, 104476, 2531004, 69265724, 2122120824, 72160283026, 2702008172582, 110631977612048, 4922281897250776, 236665779016591350, 12236187035970192634, 677311496213007409312, 39980910968200568816168
Offset: 0
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a(n)=local(A,B);A=matrix(1,1);A[1,1]=1;for(m=2,n+4,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^(2*j-1))[i-j+1,1]));));A=B); (matrix(#A,#A,r,c,if(r>=c,(A^(2*c))[r-c+1,1]))^2)[n+4,4]
Showing 1-4 of 4 results.
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