A038498 Matrix inverse of partition triangle A008284.

1, -1, 1, 0, -1, 1, 1, -1, -1, 1, 0, 1, -1, -1, 1, 0, 1, 0, -1, -1, 1, -1, 1, 1, 0, -1, -1, 1, -1, 0, 2, 0, 0, -1, -1, 1, 0, -1, 0, 2, 0, 0, -1, -1, 1, 0, -2, 1, 1, 1, 0, 0, -1, -1, 1, 1, -2, -1, 1, 1, 1, 0, 0, -1, -1, 1, 1, -1, -2, 0, 2, 0, 1, 0, 0, -1, -1, 1

Offset

1,31

Comments

Since A008284 has only ones in its first column, the sum of terms for any row n > 1 is 0. - François Marques, Feb 09 2021

Links

Table of n, a(n) for n=1..78.

Formula

T(n,n-k) = A010815(k) for k <= n/2. - François Marques, Feb 09 2021

Example

Triangle begins:
  1;
  -1,1;
  0,-1,1;
  1,-1,-1,1;
  ...

Prog

(PARI) tp(n, k) = if (n<1, 0, if (k<1, 0, if (k == n, 1, if (k > n, 0, tp(n-1, k-1) + tp(n-k, k)))));
tabl(nn) = {mtp = matrix(nn, nn, n, k, tp(n, k)); mtpi = mtp^(-1); for (n = 1, nn, for (k = 1, n, print1(mtpi[n, k], ", "); ); print(); ); } \\ Michel Marcus, Mar 04 2014

Crossrefs

Cf. A008284, A038497, A039800-A039810, A010815.

Sequence in context: A369461 A114643 A369055 * A361984 A319510 A257217

Adjacent sequences: A038495 A038496 A038497 * A038499 A038500 A038501

Keyword

sign,tabl

Author

Christian G. Bower, Feb 15 1999

Status

approved