The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A309106 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A309106

Triangular array T(m,n): number of sequences of n residues modulo m such that no nonempty subsequence sums to zero, for m>=1, n=0..m-1.
(history; published version)

#6 by N. J. A. Sloane at Sat Jul 13 00:49:55 EDT 2019

STATUS

proposed

approved

#5 by Max Alekseyev at Fri Jul 12 18:26:04 EDT 2019

STATUS

editing

proposed

#4 by Max Alekseyev at Fri Jul 12 18:24:34 EDT 2019

DATA

1, 1, 1, 1, 2, 2, 1, 3, 6, 2, 1, 4, 12, 16, 4, 1, 5, 20, 44, 10, 2, 1, 6, 30, 96, 90, 36, 6, 1, 7, 42, 174, 240, 84, 28, 4, 1, 8, 56, 288, 690, 336, 168, 48, 6, 1, 9, 72, 440, 1344, 984, 336, 144, 36, 4, 1, 10, 90, 640, 2590, 3060, 2100, 1200, 450, 100, 10

CROSSREFS

Diagonals: A000010 (n=m-1), A062955 (n=m-1, 2, starting with m=4).

#3 by Max Alekseyev at Fri Jul 12 16:29:48 EDT 2019

NAME

allocated Triangular array T(m,n): number of sequences of n residues modulo m such that no nonempty subsequence sums to zero, for Max Alekseyevm>=1, n=0..m-1.

DATA

1, 1, 1, 1, 2, 2, 1, 3, 6, 2, 1, 4, 12, 16, 4, 1, 5, 20, 44, 10, 2, 1, 6, 30, 96, 90, 36, 6, 1, 7, 42, 174, 240, 84, 28, 4, 1, 8, 56, 288, 690, 336, 168, 48, 6, 1, 9, 72, 440, 1344, 984, 336, 144, 36, 4

OFFSET

1,5

COMMENTS

T(m,n)=0 if n>=m.

LINKS

Brendan McKay et al., <a href="https://mathoverflow.net/q/119464">probability of zero subset sum</a>, MathOverflow, 2013.

CROSSREFS

Columns: A000012 (n=0), A000027 (n=1), A002378 (n=2).

Diagonals: A000010 (n=m-1), A062955 (n=m-1, starting with m=4).

KEYWORD

allocated

nonn,tabl

AUTHOR

Max Alekseyev, Jul 12 2019

STATUS

approved

editing

#2 by Max Alekseyev at Fri Jul 12 16:29:48 EDT 2019

NAME

allocated for Max Alekseyev

KEYWORD

recycled

allocated

#1 by Russ Cox at Sun Jan 27 08:30:53 EST 2019

KEYWORD

recycled

STATUS

approved