G. C. Greubel, <a href="/A192396/b192396_1.txt">Antidiagonals n = 0..50, flattened</a>

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OEIS Server: Installed first b-file as b192396.txt.

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flatten([([[A192396(n-k, k) for k in range(n+1)] for n in range(13)]) # G. C. Greubel, Jul 11 2023

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Stefano Spezia: Fixed Sagemath code

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Michel Marcus: sage : SyntaxError: closing parenthesis ']' does not match opening parenthesis '('

G. C. Greubel, <a href="/A192396/b192396_1.txt">Antidiagonals n = 0..50, flattened</a>

proposed

editing

editing

proposed

Square array T(n,, k) = floor(((k+1)^n-( - (1+(-1)^k)/2)/2) read by antidiagonals.

1: (0,1), (1,0);

3: (1,2), (2,1), (0,3), (3,0);

5: (1,4), (4,1), (2,3), (3,2);

7: (3,4), (4,3).

0, , 0, , 0, , 0, , 0, , 0,... , ... A000004;

0, , 1, , 1, , 2, , 2, , 3,... , ... A004526;

0, , 2, , 4, , 8, , 12, , 18,... , ... A007590;

0, , 4, , 13, , 32, 62, 62, 108,... , ... A036487;

0, , 8, , 40, , 128, , 312, , 648,... , ... A191903;

0, , 16, , 121, , 512, , 1562, , 3888,... , ... A191902;

. . . . . . .......

. . . . ...

with columns: A000004,, A000079,, A003462,, A004171,, A128531,, A081341,..., ... .

Antidiagonal triangle begins:

0;

0, 0;

0, 1, 0;

0, 2, 1, 0;

0, 4, 4, 2, 0;

0, 8, 13, 8, 2, 0;

0, 16, 40, 32, 12, 3, 0;

0, 32, 121, 128, 62, 18, 3, 0;

0, 64, 364, 512, 312, 108, 24, 4, 0;

Table[TableT[n_, k_]:= Floor[1/2*(([((k + +1)^n - (1 + (-+(-1)^k)/2)/2)], {n, 0, 9}, {k, 0, 9}]]];

Table[T[n-k, k], {n, 0, 12}, {k, 0, n}]//Flatten

(Magma)

A192396:= func< n, k | Floor(((k+1)^n - (1+(-1)^k)/2)/2) >;

[A192396(n-k, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Jul 11 2023

(SageMath)

def A192396(n, k): return ((k+1)^n - ((k+1)%2))//2

flatten([A192396(n-k, k) for k in range(n+1)] for n in range(13)]) # G. C. Greubel, Jul 11 2023

Rows: A000004, A004526, A007590, A036487, A191902, A191902.

Columns: A000004, A000079, A003462, A004171, A081341, A128531.

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