A117945 Triangle related to powers of 3 partitions of n.

1, 0, 1, -1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 1, -1, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, 1, 1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

Offset

0,1

Comments

Row sums are A039966.

Inverse of A117944.

Links

G. C. Greubel, Rows n = 0..50 of the triangle, flattened

Example

Triangle begins
   1;
   0,  1;
  -1,  0,  1;
   0,  0,  0,  1;
   0,  0,  0,  0, 1;
   0,  0,  0, -1, 0, 1;
  -1,  0,  0,  0, 0, 0,  1;
   0, -1,  0,  0, 0, 0,  0, 1;
   1,  0, -1,  0, 0, 0, -1, 0, 1;
   0,  0,  0,  0, 0, 0,  0, 0, 0,  1;
   0,  0,  0,  0, 0, 0,  0, 0, 0,  0, 1;
   0,  0,  0,  0, 0, 0,  0, 0, 0, -1, 0, 1;

Mathematica

M[n_, k_]:= M[n, k] = If[k>n, 0, Mod[Sum[JacobiSymbol[Binomial[n, j], 3]*JacobiSymbol[Binomial[n-j, k], 3], {j, 0, n}], 2], 0];
m:= m= With[{q=60}, Table[M[n, k], {n, 0, q}, {k, 0, q}]];
T[n_, k_]:= Inverse[m][[n+1, k+1]];
Table[T[n, k], {n, 0, 15}, {k, 0, n}]//Flatten (* G. C. Greubel, Oct 29 2021 *)

Crossrefs

Cf. A039966, A117944.

Sequence in context: A093317 A127253 A117944 * A128937 A288004 A102511

Adjacent sequences: A117942 A117943 A117944 * A117946 A117947 A117948

Keyword

sign,tabl

Author

Paul Barry, Apr 05 2006

Status

approved