A114153 Triangle, read by rows, given by the product R^-1*P^3 using triangular matrices P=A113370, R=A113389.

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

Offset

0,5

Comments

Complementary to A114152, which gives R^3*P^-1.

Links

Table of n, a(n) for n=0..44.

Example

Triangle R^-1*P^3 begins:
1;
0,1;
0,6,1;
0,48,12,1;
0,605,186,18,1;
0,11196,3892,414,24,1;
0,280440,106089,12021,732,30,1; ...
Compare to R^2 (A113392):
1;
6,1;
48,12,1;
605,186,18,1;
11196,3892,414,24,1;
280440,106089,12021,732,30,1; ...
Thus R^-1*P^3 equals R^2 shift right one column.

Prog

(PARI) 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])); R=matrix(#P, #P, r, c, if(r>=c, (P^(3*c))[r-c+1, 1])); (R^-1*P^3)[n+1, k+1]

Crossrefs

Cf. A113392 (R^2), A113370 (P), A113381 (Q), A113389 (R); A114150 (R^2*Q^-1=Q^3*P^-2), A114151 (R^-2*Q^3=Q^-1*P^2), A114152 (R^3*P^-1), A114154 (R^3*Q^-2), A114155 (Q^-2*P^3); A114156 (P^-1), A114158 (Q^-1), A114159 (R^-1).

Sequence in context: A351110 A137388 A302971 * A119832 A166141 A087253

Adjacent sequences: A114150 A114151 A114152 * A114154 A114155 A114156

Keyword

nonn,tabl

Author

Paul D. Hanna, Nov 15 2005

Status

approved