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A113355 Triangle T, read by rows, equal to the matrix square of triangle A113350, where T transforms column k of T into column k+1 of T. 8
1, 4, 1, 18, 8, 1, 112, 68, 12, 1, 965, 712, 150, 16, 1, 10957, 9270, 2184, 264, 20, 1, 156699, 147174, 37523, 4912, 410, 24, 1, 2727793, 2786270, 754171, 104476, 9280, 588, 28, 1, 56306695, 61662544, 17502145, 2531004, 235025, 15672, 798, 32, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Also, T transforms column k of A113340^2 into column k+1 of A113340^2. Column 0: T(n,0) = A113356(n) = A113346(n+1) - 1, where A113346 equals column 0 of triangle A113345 (=A113340^2).

LINKS

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

FORMULA

T(n, k) = sum_{j=0..n-k} T(n-k, j)*T(j+k-1, k-1) for n>=k>0 with T(n, 0) = A113346(n+1) - 1, for n>=0.

EXAMPLE

Triangle T begins:

1;

4,1;

18,8,1;

112,68,12,1;

965,712,150,16,1;

10957,9270,2184,264,20,1;

156699,147174,37523,4912,410,24,1;

2727793,2786270,754171,104476,9280,588,28,1;

56306695,61662544,17502145,2531004,235025,15672,798,32,1; ...

where T transforms column k of T into column k+1:

at k=0, [Q^2]*[1,4,18,112,965,...] = [1,8,68,712,9270,...];

at k=1, [Q^2]*[1,8,68,712,9270,...] = [1,12,150,2184,37523,...].

PROG

(PARI) T(n, k)=local(A, B); A=matrix(1, 1); A[1, 1]=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^(2*j-1))[i-j+1, 1])); )); A=B); (matrix(#A, #A, r, c, if(r>=c, (A^(2*c))[r-c+1, 1]))^2)[n+1, k+1]

CROSSREFS

Cf. A113340, A113350, A113356 (column 0), A113357 (column 1), A113358 (column 2), A113359 (column 3); A091351.

Sequence in context: A171589 A126331 A013631 * A201201 A077102 A258152

Adjacent sequences:  A113352 A113353 A113354 * A113356 A113357 A113358

KEYWORD

nonn,tabl

AUTHOR

Paul D. Hanna, Nov 08 2005

STATUS

approved

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Last modified May 27 02:54 EDT 2019. Contains 323597 sequences. (Running on oeis4.)