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

1,12

Links

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

Formula

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

Example

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;

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 *)

Crossrefs

Cf. A101173.

Sequence in context: A199324 A287576 A035103 * A283417 A107889 A138384

Adjacent sequences: A155030 A155031 A155032 * A155034 A155035 A155036

Keyword

nonn,tabl

Author

Mats Granvik, Jan 19 2009

Status

approved