A114159 Triangle, read by rows, equal to the matrix inverse of R=A113389.

1, -3, 1, 3, -6, 1, 35, -12, -9, 1, 396, -29, -45, -12, 1, 6237, 582, -462, -96, -15, 1, 131613, 30684, -6408, -1534, -165, -18, 1, 3518993, 1300810, -96705, -34020, -3515, -252, -21, 1, 114244366, 59124226, -764835, -944334, -102180, -6675, -357, -24, 1

Offset

0,2

Links

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

Example

Triangle R^-1 begins:
1;
-3,1;
3,-6,1;
35,-12,-9,1;
396,-29,-45,-12,1;
6237,582,-462,-96,-15,1;
131613,30684,-6408,-1534,-165,-18,1;
3518993,1300810,-96705,-34020,-3515,-252,-21,1; ...
Triangle R^-2 begins:
1;
-6,1;
24,-12,1;
79,30,-18,1;
324,356,18,-24,1;
42,5523,615,-12,-30,1;
-79346,112533,16731,640,-60,-36,1; ...

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

Crossrefs

Cf. 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), A114153 (R^-1*P^3), A114154 (R^3*Q^-2), A114155 (Q^-2*P^3); A114156 (P^-1), A114158 (Q^-1).

Sequence in context: A174505 A096713 A107726 * A236560 A291723 A359937

Adjacent sequences: A114156 A114157 A114158 * A114160 A114161 A114162

Keyword

sign,tabl

Author

Paul D. Hanna, Nov 15 2005

Status

approved