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A114155 Triangle, read by rows, given by the product Q^-2*P^3 using triangular matrices P=A113370, Q=A113381. 9
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Complementary to A114154, which gives R^3*Q^-2. Column 0 equals column 0 of P^-1 (A114157).

LINKS

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

EXAMPLE

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.

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])); (Q^-2*P^3)[n+1, k+1]

CROSSREFS

Cf. A114157 (column 0), 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); A114156 (P^-1), A114158 (Q^-1), A114159 (R^-1).

Sequence in context: A113655 A177977 A208520 * A192018 A079513 A060408

Adjacent sequences:  A114152 A114153 A114154 * A114156 A114157 A114158

KEYWORD

sign,tabl

AUTHOR

Paul D. Hanna, Nov 15 2005

STATUS

approved

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Last modified May 7 11:32 EDT 2021. Contains 343650 sequences. (Running on oeis4.)