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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A099238 Square array read by antidiagonals with rows generated by 1/(1-x-x^(k+1)).

Original entry on oeis.org

1, 1, 2, 1, 1, 4, 1, 1, 2, 8, 1, 1, 1, 3, 16, 1, 1, 1, 2, 5, 32, 1, 1, 1, 1, 3, 8, 64, 1, 1, 1, 1, 2, 4, 13, 128, 1, 1, 1, 1, 1, 3, 6, 21, 256, 1, 1, 1, 1, 1, 2, 4, 9, 34, 512, 1, 1, 1, 1, 1, 1, 3, 5, 13, 55, 1024, 1, 1, 1, 1, 1, 1, 2, 4, 7, 19, 89, 2048
Offset: 0

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Author

Paul Barry, Oct 08 2004

Keywords

Comments

Sections of rows are given by array A099233. Sums of antidiagonals yield A097939.
The triangle of diagonals terminated after reaching the repeating value is A329146. - Andrey Zabolotskiy, Sep 01 2020

Examples

			Rows begin
1,   2,   4,   8,  16,  32,  64, 128, 256, ... (A000079)
1,   1,   2,   3,   5,   8,  13,  21,  34, ... (A000045)
1,   1,   1,   2,   3,   4,   6,   9,  13, ... (A000930)
1,   1,   1,   1,   2,   3,   4,   5,   7, ... (A003269)
1,   1,   1,   1,   1,   2,   3,   4,   5, ... (A003520)

Formula

Square array T(n, k) = Sum_{j=0..floor(n/(k+1))} binomial(n-k*j, j), n, k>=0.
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