A222969 -id:A222969 - cp's OEIS frontend

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

R. H. Hardin, Mar 10 2013

nonn

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)

			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

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

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.

A222966 Number of n X 5 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.

Original entry on oeis.org

12, 48, 576, 3140, 37680, 264384, 3441888, 27387944, 361269072, 3225928864, 42721628400, 406849454892, 5367772345392, 53623428017220, 702878396190336, 7266377873987616, 94437176916813264, 1001872830089699424

Offset: 1

R. H. Hardin, Mar 10 2013

nonn

			Some solutions for n=3:
  0 0 0 1 1    0 1 0 0 1    0 0 0 1 1    0 0 1 1 1
  0 1 0 1 1    0 1 0 1 1    1 0 0 1 1    0 0 1 0 1
  0 0 0 1 1    0 1 1 1 1    0 0 1 1 1    0 1 1 1 1

R. H. Hardin, Table of n, a(n) for n = 1..21

Column 4 of A222969.

A222971 Number of 3 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.

Original entry on oeis.org

1, 6, 96, 576, 5180, 28836, 222887, 1241310, 8712264, 48837168, 328280478, 1854039060, 12126536066, 69047705664, 443482507552, 2544063717888, 16136462307440, 93109093464048, 585311170019020, 3393940344415872

Offset: 1

R. H. Hardin, Mar 10 2013

nonn

			Some solutions for n=3:
  0 1 0 1    0 0 0 1    0 1 1 1    0 0 0 1    0 0 1 1
  0 1 1 1    0 1 1 1    0 0 0 1    0 0 1 1    0 1 1 1
  0 1 0 1    0 0 0 1    0 1 1 1    0 1 0 1    0 1 1 1

R. H. Hardin, Table of n, a(n) for n = 1..24

Row 3 of A222969.

A222965 Number of n X 4 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.

Original entry on oeis.org

6, 16, 96, 314, 1884, 7344, 46512, 199912, 1281096, 6018524, 38837844, 192182076, 1239097956, 6379184870, 40998506544, 217140146844, 1387598473608, 7510403679888, 47773334036628, 262699726452550, 1662636615068856

Offset: 1

R. H. Hardin, Mar 10 2013

			Some solutions for n=3:
  0 0 1 1    0 1 0 1    0 0 0 1    0 0 1 0    0 0 1 0
  0 0 1 1    0 1 0 1    0 0 1 1    1 0 1 1    0 0 0 1
  0 1 1 1    0 1 0 1    0 0 1 1    0 0 1 1    0 0 1 0

Column 3 of A222969.

A222967 Number of n X 6 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.

Original entry on oeis.org

28, 185, 5180, 53292, 1492176, 21852384, 687269268, 11877013537, 379255412732, 7601814965106, 242873494106544

Offset: 1

R. H. Hardin, Mar 10 2013

			Some solutions for n=3:
  0 0 0 0 1 1    0 0 1 0 1 0    0 0 1 1 1 0    0 0 0 0 0 1
  0 1 0 1 0 1    0 1 0 1 0 1    0 0 1 1 0 1    0 1 0 0 1 1
  0 1 1 1 1 1    0 0 1 1 1 0    0 0 1 1 1 0    1 0 0 1 0 1

Column 5 of A222969.

A222968 Number of n X 7 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.

Original entry on oeis.org

54, 534, 28836, 487830, 26342820, 677339136, 41972251734, 1306606331404, 82298403509112, 3041055175823616, 191470088044451700

Offset: 1

R. H. Hardin, Mar 10 2013

			Some solutions for n=3:
  1 0 0 0 0 1 1    0 0 1 0 0 0 1    1 0 0 0 0 1 1
  0 0 0 0 0 0 1    0 0 0 1 1 0 1    1 0 1 1 0 1 1
  1 0 0 1 1 1 1    0 0 1 0 0 0 1    1 1 0 1 1 1 1

Column 6 of A222969.

A222972 Number of 4 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.

Original entry on oeis.org

1, 10, 314, 3140, 53292, 487830, 6811479, 62248790, 767197516, 7042095920, 81955369777, 758479227700, 8507298585600, 79472821382440, 870035427428542, 8203118157997530

Offset: 1

R. H. Hardin, Mar 10 2013

			Some solutions for n=3:
  0 0 1 0    1 0 1 1    0 0 1 0    0 0 1 1    0 0 1 1
  0 1 0 1    1 0 1 1    0 0 1 1    0 0 0 1    0 1 0 1
  0 1 1 1    1 0 1 1    0 1 1 1    0 0 0 1    0 0 0 1
  0 0 1 1    1 0 1 1    0 0 1 0    0 1 1 1    0 1 1 1

Row 4 of A222969.

A222973 Number of 5 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.

Original entry on oeis.org

1, 20, 1884, 37680, 1492176, 26342820, 810566001, 14317221700, 374392387808, 6675906932160, 162189676788683, 2927729818922000, 67871228115916800, 1241683361279242560

Offset: 1

R. H. Hardin, Mar 10 2013

			Some solutions for n=3:
  0 0 1 0    0 0 0 1    0 0 1 0    0 0 1 0    0 0 1 1
  0 1 0 1    0 0 0 1    0 0 1 0    0 0 1 0    0 0 1 0
  0 1 0 1    0 0 1 0    0 1 1 1    0 0 1 1    0 0 1 0
  0 0 1 1    0 1 0 1    0 1 1 1    1 0 1 1    0 0 1 1
  0 1 1 1    0 1 1 1    0 1 1 1    0 0 1 1    1 0 1 1

Row 5 of A222969.

A222974 Number of 6 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.

Original entry on oeis.org

1, 36, 7344, 264384, 21852384, 677339136, 41252032201, 1279444594428, 63987904860942, 2004349575346776

Offset: 1

R. H. Hardin, Mar 10 2013

			Some solutions for n=3:
  0 0 1 1    0 0 1 1    0 1 1 1    0 0 1 1    0 0 1 0
  0 0 0 1    1 0 1 1    0 0 1 0    0 0 0 1    0 0 0 1
  0 1 1 1    1 0 1 1    1 0 1 1    0 1 0 1    0 0 1 0
  0 0 1 1    0 0 1 1    1 0 1 1    0 0 1 1    0 1 1 1
  0 1 0 1    0 1 1 1    0 1 1 1    0 1 1 1    0 0 1 0
  0 1 1 1    1 0 1 1    0 1 1 1    0 0 1 1    1 0 1 1

Row 6 of A222969.

cp's OEIS Frontend

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.

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A222966 Number of n X 5 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.

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A222971 Number of 3 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.

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A222965 Number of n X 4 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.

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A222967 Number of n X 6 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.

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A222968 Number of n X 7 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.

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A222972 Number of 4 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.

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A222973 Number of 5 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.

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A222974 Number of 6 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.

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