A114156
Triangle, read by rows, equal to the matrix inverse of P=A113370.
Original entry on oeis.org
1, -1, 1, 3, -4, 1, 6, 0, -7, 1, -8, 38, -21, -10, 1, -501, 692, -119, -60, -13, 1, -13623, 14910, -420, -735, -117, -16, 1, -409953, 401802, 22911, -12470, -2080, -192, -19, 1, -14544683, 13278520, 1577527, -255570, -51064, -4424, -285, -22, 1
Offset: 0
Triangle P^-1 begins:
1;
-1,1;
3,-4,1;
6,0,-7,1;
-8,38,-21,-10,1;
-501,692,-119,-60,-13,1;
-13623,14910,-420,-735,-117,-16,1;
-409953,401802,22911,-12470,-2080,-192,-19,1; ...
Triangle P^-2 begins:
1;
-2,1;
10,-8,1;
-9,28,-14,1;
-177,160,28,-20,1;
-2307,1366,455,10,-26,1;
-38874,15982,8666,660,-26,-32,1; ...
-
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); (P^-1)[n+1,k+1]
A114155
Triangle, read by rows, given by the product Q^-2*P^3 using triangular matrices P=A113370, Q=A113381.
Original entry on oeis.org
1, -1, 1, 3, 2, 1, 6, 6, 5, 1, -8, 37, 45, 8, 1, -501, 429, 635, 120, 11, 1, -13623, 7629, 12815, 2556, 231, 14, 1, -409953, 185776, 343815, 71548, 6556, 378, 17, 1, -14544683, 5817106, 11651427, 2508528, 233706, 13391, 561, 20, 1
Offset: 0
Triangle Q^-2*P^3 begins:
1;
-1,1;
3,2,1;
6,6,5,1;
-8,37,45,8,1;
-501,429,635,120,11,1;
-13623,7629,12815,2556,231,14,1;
-409953,185776,343815,71548,6556,378,17,1; ...
Compare to Q (A113381):
1;
2,1;
6,5,1;
37,45,8,1;
429,635,120,11,1;
7629,12815,2556,231,14,1;...
Thus Q^-2*P^3 shift left one column equals Q.
-
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])); (Q^-2*P^3)[n+1,k+1]
Showing 1-2 of 2 results.
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