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A099238

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

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

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OFFSET

0,3

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

LINKS

Table of n, a(n) for n=0..77.

FORMULA

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

EXAMPLE

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)

CROSSREFS

Sequence in context: A192005 A333810 A205592 * A306846 A327315 A141450

Adjacent sequences: A099235 A099236 A099237 * A099239 A099240 A099241

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Oct 08 2004

STATUS

approved