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.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

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.

Cf. A000005, A000041, A138364, A320387, A360672, A360675, A363626.

Sequence in context: A290419 A159553 A327727 * A112510 A284449 A011949

Adjacent sequences: A222967 A222968 A222969 * A222971 A222972 A222973

Keyword

nonn

Author

R. H. Hardin, Mar 10 2013

Status

approved