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A068913 Square array read by antidiagonals of number of k step walks (each step +/-1 starting from 0) which are never more than n or less than -n. 10
1, 0, 1, 0, 2, 1, 0, 2, 2, 1, 0, 4, 4, 2, 1, 0, 4, 6, 4, 2, 1, 0, 8, 12, 8, 4, 2, 1, 0, 8, 18, 14, 8, 4, 2, 1, 0, 16, 36, 28, 16, 8, 4, 2, 1, 0, 16, 54, 48, 30, 16, 8, 4, 2, 1, 0, 32, 108, 96, 60, 32, 16, 8, 4, 2, 1, 0, 32, 162, 164, 110, 62, 32, 16, 8, 4, 2, 1, 0, 64, 324, 328, 220, 124, 64, 32, 16, 8, 4, 2, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Alois P. Heinz, Antidiagonals n = 0..200, flattened

FORMULA

Starting with T(n, 0)=1; if (k-n) is negative or even then T(n, k)=2T(n, k-1); otherwise T(n, k)=2T(n, k-1)-A061897(n-1, (k-n-1)/2); so for n>=k T(n, k)=2^k.

EXAMPLE

Rows start:

1,0,0,0,0,...

1,2,2,4,4,...

1,2,4,6,12,...

1,2,4,8,14,...

...

CROSSREFS

Cf. early rows: A000007, A016116 (without initial term), A068911, A068912, A216212, A216241, A235701.

Central and lower diagonals are A000079, higher diagonals include A000918, A028399.

Sequence in context: A289281 A212957 A035393 * A128306 A305152 A170983

Adjacent sequences:  A068910 A068911 A068912 * A068914 A068915 A068916

KEYWORD

nonn,tabl

AUTHOR

Henry Bottomley, Mar 06 2002

STATUS

approved

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Last modified December 9 00:32 EST 2019. Contains 329871 sequences. (Running on oeis4.)