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A099238 Square array read by antidiagonals with rows generated by 1/(1-x-x^(k+1)). 4
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Sections of rows are given by array A099233. Sums of antidiagonals yield A097939.

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: A249694 A192005 A205592 * A141450 A209690 A061462

Adjacent sequences:  A099235 A099236 A099237 * A099239 A099240 A099241

KEYWORD

easy,nonn,tabl,changed

AUTHOR

Paul Barry, Oct 08 2004

STATUS

approved

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Last modified December 7 19:05 EST 2016. Contains 278895 sequences.