A334016 -id:A334016 - cp's OEIS frontend

A338276 a(n) is the number of odd terms in the n-th column of A334016.

2, 2, 4, 6, 6, 6, 8, 10, 12, 14, 12, 10, 10, 10, 16, 22, 22, 22, 20, 18, 18, 18, 16, 14, 16, 18, 20, 22, 22, 22, 32, 42, 44, 46, 36, 26, 26, 26, 32, 38, 36, 34, 28, 22, 22, 22, 24, 26, 26, 26, 28, 30, 30, 30, 32, 34, 40, 46, 44, 42, 42, 42, 64, 86, 86, 86, 68

Offset: 1

Peter Kagey, Oct 20 2020

All terms are even.

Conjecture: a(2^n - 1) = 2^n for n > 0. - Peter Kagey, Oct 22 2020

			Table for A334016 begins:
n\k|   1    2     3      4       5        6         7          8
---+------------------------------------------------------------
  1|   1    1     6     35     237     1684     12557      96605
  2|   1    4    21    139     978     7239     55423     435550
  3|   2   10    65    451    3339    25559    200922    1611624
  4|   4   25   179   1337   10325    81716    658918    5394051
  5|   8   60   470   3725   30018   245220   2027447   16935981
  6|  16  140  1189   9958   83518   703635   5961973   50811786
  7|  32  320  2926  25802  224831  1951587  16938814  147261146
  8|  64  720  7048  65241  589701  5269220  46826316  415175289
a(1) = 2 because the first column has two odd values: (1,1).
a(2) = 2 because the second column has two odd values: (1,25).
a(3) = 4 because the third column has four odd values: (35,139,451,1337).

Peter Kagey, Table of n, a(n) for n = 1..8192
Peter Kagey, Parity bitmap of first 2048 rows and 1024 columns of A334016. (Even and odd entries and represented by black and white pixels respectively.)

Cf. A334016.

Cf. A334001 is analogous for A279212.

A334017 Table read by antidiagonals upward: T(n,k) is the number of ways to move a chess queen from (1,1) to (n,k) in the first quadrant using only up, right, and diagonal up-left moves.

Original entry on oeis.org

1, 1, 2, 2, 5, 10, 4, 13, 33, 63, 8, 32, 98, 240, 454, 16, 76, 269, 777, 1871, 3539, 32, 176, 702, 2295, 6420, 15314, 29008, 64, 400, 1768, 6393, 19970, 54758, 129825, 246255, 128, 896, 4336, 17088, 58342, 176971, 478662, 1129967, 2145722, 256, 1984, 10416

Offset: 1

Peter Kagey, Apr 12 2020

First row is A175962.

			Table begins:
n\k|  1   2     3      4       5        6         7          8
---+----------------------------------------------------------
  1|  1   2    10     63     454     3539     29008     246255
  2|  1   5    33    240    1871    15314    129825    1129967
  3|  2  13    98    777    6420    54758    478662    4266102
  4|  4  32   269   2295   19970   176971   1593093   14532881
  5|  8  76   702   6393   58342   536080   4965056   46345046
  6| 16 176  1768  17088  163041  1550809  14765863  140982374
  7| 32 400  4336  44280  440602  4332221  42373370  413689403
  8| 64 896 10416 111984 1159580 11771312 118190333 1179448443
For example, the T(2,2) = 5 sequences of permissible queen's moves from (1,1) to (2,2) are:
(1,1) -> (1,2) -> (2,2),
(1,1) -> (2,1) -> (1,2) -> (2,2),
(1,1) -> (2,1) -> (2,2),
(1,1) -> (2,1) -> (3,1) -> (2,2), and
(1,1) -> (3,1) -> (2,2).

Peter Kagey, Table of n, a(n) for n = 1..10011 (first 141 antidiagonals)
Peter Kagey, Parity bitmap for first 1024 rows and columns. (Even and odd entries and represented by black and white pixels respectively.)

Cf. A175962.
Cf. A035002 (up, right), A059450 (right, up-left), A132439 (up, right, up-right), A279212 (up, right, up-left), A334016 (right, up-right, up-left).
A033877 is the analog for king moves. For both king and queen moves, A094727 is the length of the longest sequence of moves.

cp's OEIS Frontend

A338276 a(n) is the number of odd terms in the n-th column of A334016.

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