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A222970
Number of 1 X (n+1) 0..1 arrays with every row least squares fitting to a positive-slope straight line and every column least squares fitting to a zero- or positive-slope straight line, with a single point array taken as having zero slope.
8
1, 2, 6, 12, 28, 54, 119, 230, 488, 948, 1979, 3860, 7978, 15624, 32072, 63014, 128746, 253588, 516346, 1019072, 2069590, 4091174, 8291746, 16412668, 33210428, 65808044, 132985161, 263755984, 532421062, 1056789662, 2131312530, 4233176854
OFFSET
1,2
COMMENTS
From Gus Wiseman, Jun 16 2023: (Start)
Also appears to be the number of integer compositions of n + 2 with weighted sum greater than reverse-weighted sum, where the weighted sum of a sequence (y_1,...,y_k) is Sum_{i=1..k} i * y_i, and the reverse is Sum_{i=1..k} i * y_{k-i+1}. The a(1) = 1 through a(4) = 12 compositions are:
(21) (31) (32) (42)
(211) (41) (51)
(221) (231)
(311) (312)
(1211) (321)
(2111) (411)
(1311)
(2121)
(2211)
(3111)
(12111)
(21111)
The version for partitions is A144300, strict A111133.
(End)
LINKS
EXAMPLE
Some solutions for n=3:
0 1 0 1 0 1 1 1 0 0 1 0 0 0 1 1 0 0 0 1
CROSSREFS
For >= instead of > we have A222855.
The case of equality is A222955.
Row 1 of A222969.
A053632 counts compositions by weighted sum (or reverse-weighted sum).
A264034 counts partitions by weighted sum, reverse A358194.
A304818 gives weighted sum of prime indices, reverse A318283.
Sequence in context: A290419 A159553 A327727 * A112510 A284449 A011949
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 10 2013
STATUS
approved