A330885 Square array T(n,k) read by antidiagonals upwards: T(n,0)=1; T(n,1) = n+1; T(n,2) = 2n+1, T(n,k>2) = T(n,k-1) - T(n,k-2) - T(n,k-3).

1, 1, 1, 1, 2, 1, 1, 3, 3, -1, 1, 4, 5, 0, -3, 1, 5, 7, 1, -5, -3, 1, 6, 9, 2, -7, -8, 1, 1, 7, 11, 3, -9, -13, -3, 7, 1, 8, 13, 4, -11, -18, -7, 10, 9, 1, 9, 15, 5, -13, -23, -11, 13, 21, 1, 1, 10, 17, 6, -15, -28, -15, 16, 33, 14, -15

Offset: 0

Author

Bob Selcoe, May 05 2020

Keywords

• sign
• tabl

Examples

			Array starts:
1  1   1  -1   -3   -3    1   7   9   1  -15   -25
1  2   3   0   -5   -8   -3  10  21  14  -17   -52
1  3   5   1   -7  -13   -7  13  33  27  -19   -79
1  4   7   2   -9  -18  -11  16  45  40  -21  -106
1  5   9   3  -11  -23  -15  19  57  53  -23  -133
1  6  11   4  -13  -28  -19  22  69  66  -25  -160
1  7  13   5  -15  -33  -23  25  81  79  -27  -187
		

Crossrefs

Cf. A078016, A180735.

Columns k: A000012 (k=0), A000027 (k=1), A005408 (k=2), A023443 (k=3), A165747 (k=4), -A016885 (k=5), -A004767 (k=6), A016777 (k=7), A017629 (k=8), A190991 (k=9).

Programs

Mathematica

T[n_, k_]:= T[n, k]= If[k<3, k*n+1, T[n, k-1] - T[n, k-2] - T[n, k-3]];
Table[T[n-k, k], {n,0,12}, {k,0,n}]//Flatten (* G. C. Greubel, May 26 2020 *)

Formula

T(0,k) = A180735(k-1).

T(n,k) - T(n-1,k) = -A078016(k+1).