A155033 Matrix inverse of A155031.

1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 3, 2, 1, 1, 0, 4, 3, 2, 1, 1, 0, 10, 7, 4, 2, 1, 1, 0, 18, 13, 7, 4, 2, 1, 1, 0, 37, 26, 15, 8, 4, 2, 1, 1, 0, 71, 51, 29, 15, 8, 4, 2, 1, 1, 0, 146, 104, 59, 31, 16, 8, 4, 2, 1, 1, 0, 285, 203, 115, 61, 31, 16, 8, 4, 2, 1, 1, 0, 577, 411, 233, 123, 63, 32, 16, 8, 4, 2, 1, 1

Offset: 1

Author

Mats Granvik, Jan 19 2009

Keywords

• nonn
• tabl

Examples

			Table begins and row sums are:
  1                            =  1;
  0,  1                        =  1;
  0,  1,  1                    =  2;
  0,  1,  1,  1                =  3;
  0,  3,  2,  1, 1             =  7;
  0,  4,  3,  2, 1, 1          = 11;
  0, 10,  7,  4, 2, 1, 1       = 25;
  0, 18, 13,  7, 4, 2, 1, 1    = 46;
  0, 37, 26, 15, 8, 4, 2, 1, 1 = 94;
		

Links

• G. C. Greubel, Rows n = 1..50 of the triangle, flattened

Crossrefs

Cf. A101173.

Programs

Mathematica

A155031[n_, k_]:= If[k>n, 0, If[k==n, 1, If[k==1 || Mod[n, k]==0, 0, -1]]];
A155033:= Inverse[Table[A155031[n, k], {n,30}, {k,30}]];
Table[A155033[[n, k]], {n,15}, {k,n}]//Flatten (* G. C. Greubel, Mar 15 2021 *)

Formula

Sum_{k=1..n} T(n,k) = A101173(n). - G. C. Greubel, Mar 15 2021