A091603 - OEIS

%I #9 Nov 27 2021 02:26:06

%S 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,

%T 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,

%U 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

%N Matrix inverse of triangle A091602.

%H G. C. Greubel, <a href="/A091603/b091603.txt">Table of n, a(n) for n = 1..1275</a>

%e Triangle begins as:

%e    1;

%e   -1,  1;

%e   -2,  0,  1;

%e    0, -2,  0,  1;

%e    1, -2, -1,  0,  1;

%e    3, -1, -2, -1,  0,  1;

%e    4,  0, -2, -1, -1,  0,  1;

%e    3,  2,  0, -2, -1, -1,  0,  1;

%e    3,  3,  0, -1, -1, -1, -1,  0,  1;

%e    0,  4,  2,  0, -1, -1, -1, -1,  0,  1;

%e    0,  4,  2,  1, -1,  0, -1, -1, -1,  0,  1;

%e   -3,  3,  3,  2,  1, -1,  0, -1, -1, -1,  0,  1;

%e   -4,  3,  3,  2,  1,  0,  0,  0, -1, -1, -1,  0,  1;

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

%e   -9,  1,  3,  2,  2,  1,  0,  1,  0,  0, -1, -1, -1,  0,  1;

%t 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 t[n_, k_]:= t[n, k]= b[n, 1, k] - b[n, 1, k-1]; (* t = A091602 *)

%t M:= With[{p = 30}, Table[t[n, k], {n, p}, {k, p}]];

%t T:= Inverse[M];

%t Table[T[[n, k]], {n, 15}, {k, n}]//Flatten (* _G. C. Greubel_, Nov 26 2021 *)

%Y Cf. A091602, A091612 (column 1).

%K sign,tabl

%O 1,4

%A _Christian G. Bower_, Jan 23 2004