A113378
Triangle, read by rows, equal to the matrix cube of A113370.
Original entry on oeis.org
1, 3, 1, 15, 12, 1, 136, 168, 21, 1, 1998, 3190, 483, 30, 1, 41973, 80136, 13615, 960, 39, 1, 1166263, 2553162, 469476, 35785, 1599, 48, 1, 40747561, 99579994, 19419225, 1562220, 74074, 2400, 57, 1, 1726907675, 4624245724, 944233801, 79072620
Offset: 0
Triangle A113370^3 begins:
1;
3,1;
15,12,1;
136,168,21,1;
1998,3190,483,30,1;
41973,80136,13615,960,39,1;
1166263,2553162,469476,35785,1599,48,1;
40747561,99579994,19419225,1562220,74074,2400,57,1;
1726907675,4624245724,944233801,79072620,3908034,132856,3363,66,1;
-
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^3)[n+1,k+1]
A114158
Triangle, read by rows, equal to the matrix inverse of Q=A113381.
Original entry on oeis.org
1, -2, 1, 4, -5, 1, 21, -5, -8, 1, 130, 20, -32, -11, 1, 1106, 840, -260, -77, -14, 1, 10044, 24865, -2584, -1089, -140, -17, 1, -18366, 823383, -12828, -21428, -2737, -221, -20, 1, -9321125, 31847653, 1160956, -523831, -73458, -5474, -320, -23, 1
Offset: 0
Triangle Q^-1 begins:
1;
-2,1;
4,-5,1;
21,-5,-8,1;
130,20,-32,-11,1;
1106,840,-260,-77,-14,1;
10044,24865,-2584,-1089,-140,-17,1;
-18366,823383,-12828,-21428,-2737,-221,-20,1; ...
Triangle Q^-2 begins:
1;
-4,1;
18,-10,1;
20,30,-16,1;
-139,255,24,-22,1;
-3945,3085,544,0,-28,1;
-99849,51015,12444,671,-42,-34,1; ...
-
T(n,k)=local(P,Q,R,W);P=Mat(1);for(m=2,n+1,W=matrix(m,m); for(i=1,m, for(j=1,i,if(i<3 || j==i || j>m-1,W[i,j]=1,if(j==1, W[i,1]=1,W[i,j]=(P^(3*j-2))[i-j+1,1]));));P=W); Q=matrix(#P,#P,r,c,if(r>=c,(P^(3*c-1))[r-c+1,1])); (Q^-1)[n+1,k+1]
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
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;
-
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]
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
-
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]