A091603 Matrix inverse of triangle A091602.

1, -1, 1, -2, 0, 1, 0, -2, 0, 1, 1, -2, -1, 0, 1, 3, -1, -2, -1, 0, 1, 4, 0, -2, -1, -1, 0, 1, 3, 2, 0, -2, -1, -1, 0, 1, 3, 3, 0, -1, -1, -1, -1, 0, 1, 0, 4, 2, 0, -1, -1, -1, -1, 0, 1, 0, 4, 2, 1, -1, 0, -1, -1, -1, 0, 1, -3, 3, 3, 2, 1, -1, 0, -1, -1, -1, 0, 1, -4, 3, 3, 2, 1, 0, 0, 0, -1, -1, -1, 0, 1

Offset: 1

Author

Christian G. Bower, Jan 23 2004

Keywords

• sign
• tabl

Examples

			Triangle begins as:
   1;
  -1,  1;
  -2,  0,  1;
   0, -2,  0,  1;
   1, -2, -1,  0,  1;
   3, -1, -2, -1,  0,  1;
   4,  0, -2, -1, -1,  0,  1;
   3,  2,  0, -2, -1, -1,  0,  1;
   3,  3,  0, -1, -1, -1, -1,  0,  1;
   0,  4,  2,  0, -1, -1, -1, -1,  0,  1;
   0,  4,  2,  1, -1,  0, -1, -1, -1,  0,  1;
  -3,  3,  3,  2,  1, -1,  0, -1, -1, -1,  0,  1;
  -4,  3,  3,  2,  1,  0,  0,  0, -1, -1, -1,  0,  1;
  -7,  2,  3,  2,  2,  1,  0,  0,  0, -1, -1, -1,  0,  1;
  -9,  1,  3,  2,  2,  1,  0,  1,  0,  0, -1, -1, -1,  0,  1;
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1275

Crossrefs

Cf. A091602, A091612 (column 1).

Programs

Mathematica

b[n_, i_, k_]:= b[n, i, k]= If[n==0, 1, If[i>n, 0, Sum[b[n-i*j, i+1, Min[k, Quotient[n-i*j, i+1]]], {j,0,k}]]];
t[n_, k_]:= t[n, k]= b[n, 1, k] - b[n, 1, k-1]; (* t = A091602 *)
M:= With[{p = 30}, Table[t[n, k], {n, p}, {k, p}]];
T:= Inverse[M];
Table[T[[n, k]], {n, 15}, {k, n}]//Flatten (* G. C. Greubel, Nov 26 2021 *)