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A091603
Matrix inverse of triangle A091602.
3
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, 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, 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
OFFSET
1,4
LINKS
EXAMPLE
Triangle begins as:
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, 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, 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;
-7, 2, 3, 2, 2, 1, 0, 0, 0, -1, -1, -1, 0, 1;
-9, 1, 3, 2, 2, 1, 0, 1, 0, 0, -1, -1, -1, 0, 1;
MATHEMATICA
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[n_, k_]:= t[n, k]= b[n, 1, k] - b[n, 1, k-1]; (* t = A091602 *)
M:= With[{p = 30}, Table[t[n, k], {n, p}, {k, p}]];
T:= Inverse[M];
Table[T[[n, k]], {n, 15}, {k, n}]//Flatten (* G. C. Greubel, Nov 26 2021 *)
CROSSREFS
Cf. A091602, A091612 (column 1).
Sequence in context: A039995 A035232 A359269 * A370884 A325036 A194942
KEYWORD
sign,tabl
AUTHOR
Christian G. Bower, Jan 23 2004
STATUS
approved