A155033 - OEIS

%I #6 Mar 15 2021 21:30:33

%S 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,

%T 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,

%U 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

%N Matrix inverse of A155031.

%H G. C. Greubel, <a href="/A155033/b155033.txt">Rows n = 1..50 of the triangle, flattened</a>

%F Sum_{k=1..n} T(n,k) = A101173(n). - _G. C. Greubel_, Mar 15 2021

%e Table begins and row sums are:

%e   1                            =  1;

%e   0,  1                        =  1;

%e   0,  1,  1                    =  2;

%e   0,  1,  1,  1                =  3;

%e   0,  3,  2,  1, 1             =  7;

%e   0,  4,  3,  2, 1, 1          = 11;

%e   0, 10,  7,  4, 2, 1, 1       = 25;

%e   0, 18, 13,  7, 4, 2, 1, 1    = 46;

%e   0, 37, 26, 15, 8, 4, 2, 1, 1 = 94;

%t A155031[n_, k_]:= If[k>n, 0, If[k==n, 1, If[k==1 || Mod[n, k]==0, 0, -1]]];

%t A155033:= Inverse[Table[A155031[n, k], {n,30}, {k,30}]];

%t Table[A155033[[n, k]], {n,15}, {k,n}]//Flatten (* _G. C. Greubel_, Mar 15 2021 *)

%Y Cf. A101173.

%K nonn,tabl

%O 1,12

%A _Mats Granvik_, Jan 19 2009