A155031 -id:A155031 - cp's OEIS frontend

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

Mats Granvik, Jan 19 2009

			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;

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

Cf. A101173.

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 *)

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

A155029 Complement to A051731 with the identity matrix A023531 included.

Original entry on oeis.org

1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Mats Granvik, Jan 19 2009

			Table begins:
  1;
  0, 1;
  0, 1, 1;
  0, 0, 1, 1;
  0, 1, 1, 1, 1;
  0, 0, 0, 1, 1, 1;
  0, 1, 1, 1, 1, 1, 1;
  0, 0, 1, 0, 1, 1, 1, 1;
  0, 1, 0, 1, 1, 1, 1, 1, 1;

G. C. Greubel, Rows n = 1..30 of the triangle, flattened

Cf. A023531, A051731, A155031.

[k eq n select 1 else (k eq 0 or n mod k eq 0) select 0 else 1: k in [1..n], n in [1..20]]; // G. C. Greubel, Mar 07 2021

Table[If[k==n, 1, If[k==0, 0, If[Mod[n, k]==0, 0, 1]]], {n, 20}, {k, n}]//Flatten (* G. C. Greubel, Mar 07 2021 *)

flatten([[1 if k==n else 0 if (k==0 or n%k==0) else 1 for k in [1..n]] for n in [1..20]]) # G. C. Greubel, Mar 07 2021

T(n, k) = 0 if n==0 (mod k) otherwise 1 with T(n, n) = 1 and T(n, 1) = 0. - G. C. Greubel, Mar 07 2021

cp's OEIS Frontend

A155033 Matrix inverse of A155031.

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