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A091603
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Matrix inverse of triangle A091602.
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3
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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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,4
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LINKS
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EXAMPLE
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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;
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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