A227263 -id:A227263 - cp's OEIS frontend

A227259 Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having a sum of two or less, with rows and columns of the latter in lexicographically nondecreasing order.

3, 9, 23, 50, 96, 168, 274, 423, 625, 891, 1233, 1664, 2198, 2850, 3636, 4573, 5679, 6973, 8475, 10206, 12188, 14444, 16998, 19875, 23101, 26703, 30709, 35148, 40050, 45446, 51368, 57849, 64923, 72625, 80991, 90058, 99864, 110448, 121850, 134111

Offset: 1

R. H. Hardin, Jul 04 2013

nonn

Conjecture: a(n) is also the number of length n strings of {0,1,2} with digit sum <= 4 (holds if the empirical formula holds). - Daniel T. Martin, May 24 2023

			Some solutions for n=4:
  1 0   1 1   1 1   1 1   1 1   1 0   1 1   1 1   0 0   1 1
  1 1   1 0   1 0   1 1   1 1   1 1   1 1   0 1   0 0   1 1
  1 1   0 0   0 1   1 1   0 1   0 1   1 1   0 0   0 0   0 0
  0 1   0 0   0 1   1 0   0 1   0 1   0 0   0 0   0 0   0 0

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

Column 2 of A227263.

Cf. A105163.

Empirical: a(n) = (1/24)*n^4 + (5/12)*n^3 + (11/24)*n^2 + (13/12)*n + 1.

G.f.: x*(3 - 6*x + 8*x^2 - 5*x^3 + x^4) / (1 - x)^5. (Conjecture from Colin Barker, Sep 07 2018)

A227260 Number of nX3 0,1 arrays indicating 2X2 subblocks of some larger (n+1)X4 binary array having a sum of two or less, with rows and columns of the latter in lexicographically nondecreasing order.

Original entry on oeis.org

4, 23, 98, 353, 1111, 3136, 8065, 19146, 42385, 88282, 174361, 328741, 595043, 1038979, 1757024, 2887631, 4625512, 7239575, 11095178, 16681436, 24644396, 35826978, 51316667, 72502032, 101139243, 139429856, 190111239, 256561119

Offset: 1

R. H. Hardin Jul 04 2013

nonn

Column 3 of A227263

			Some solutions for n=4
..1..1..0....1..1..1....1..1..0....1..0..0....1..1..0....1..1..1....1..1..0
..1..1..1....1..0..0....1..1..1....0..1..0....0..1..1....1..0..1....1..1..1
..1..1..1....1..1..0....1..1..1....0..1..1....0..1..1....0..1..1....1..1..1
..0..0..0....0..1..0....1..1..1....0..0..1....0..0..1....0..0..1....0..0..1

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

Empirical: a(n) = (1/90720)*n^9 + (11/40320)*n^8 + (53/30240)*n^7 + (73/2880)*n^6 + (301/4320)*n^5 - (2683/5760)*n^4 + (448811/90720)*n^3 + (1613/1120)*n^2 - (83207/2520)*n + 33 for n>5

A227261 Number of n X 4 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 5 binary array having a sum of two or less, with rows and columns of the latter in lexicographically nondecreasing order.

Original entry on oeis.org

5, 50, 353, 2201, 11932, 57146, 244818, 951917, 3403038, 11297855, 35123154, 102968348, 286360987, 759331583, 1928166887, 4706232142, 11076831313, 25210805133, 55622829033, 119222502647, 248739253915, 506020952898

Offset: 1

R. H. Hardin, Jul 04 2013

nonn

Column 4 of A227263.

			Some solutions for n=4
..1..0..0..0....1..1..1..0....1..1..0..0....1..1..1..0....1..1..1..1
..1..1..1..0....1..1..0..0....1..0..0..0....1..1..1..0....1..1..1..0
..1..1..1..1....1..0..0..0....1..0..1..1....1..1..1..0....0..0..0..0
..1..1..1..1....1..1..0..0....1..0..1..1....1..0..1..1....0..0..0..1

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

Cf. A227263.

Empirical: a(n) = (1/1689515283456000)*n^19 + (43/1067062284288000)*n^18 + (1/1097800704000)*n^17 + (1/24908083200)*n^16 + (2161/2615348736000)*n^15 + (7723/10461394944000)*n^14 + (76931/201180672000)*n^13 + (38351/48283361280)*n^12 - (9767641/402361344000)*n^11 + (9434683/6967296000)*n^10 - (3668820107/402361344000)*n^9 - (5124736597/80472268800)*n^8 + (150774753091/72648576000)*n^7 - (42587741190289/3923023104000)*n^6 - (18276563116219/163459296000)*n^5 + (6577553955799/3113510400)*n^4 - (743180805841567/51459408000)*n^3 + (63341814516853/1286485200)*n^2 - (326223749821/4476780)*n + 17722 for n>9.

A227262 Number of nX5 0,1 arrays indicating 2X2 subblocks of some larger (n+1)X6 binary array having a sum of two or less, with rows and columns of the latter in lexicographically nondecreasing order.

Original entry on oeis.org

6, 96, 1111, 11932, 112349, 937865, 6961606, 46364258, 280471755, 1557597103, 8014162577, 38505244717, 173924889597, 742804988619, 3014292672706, 11671178123287, 43274437542484, 154133395370348, 528811622382841

Offset: 1

R. H. Hardin Jul 04 2013

nonn

Column 5 of A227263

			Some solutions for n=4
..1..1..0..0..0....1..1..1..0..0....1..1..1..1..0....1..1..1..1..1
..1..1..0..0..0....1..0..0..0..0....1..0..1..1..1....1..1..0..0..1
..1..1..0..0..0....0..0..0..0..1....0..0..0..0..1....1..1..1..1..0
..1..0..0..1..1....0..0..0..0..0....0..1..1..0..1....0..1..1..1..0

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical polynomial of degree 39

Empirical polynomial of degree 39 (see link above)

A227258 Number of n X n 0,1 arrays indicating 2X2 subblocks of some larger (n+1)X(n+1) binary array having a sum of two or less, with rows and columns of the latter in lexicographically nondecreasing order.

Original entry on oeis.org

2, 9, 98, 2201, 112349, 13855163, 4307345460

Offset: 1

R. H. Hardin Jul 04 2013

nonn

Diagonal of A227263

			Some solutions for n=4
..1..1..1..0....1..1..1..1....1..1..1..1....1..1..1..0....1..1..0..0
..1..0..0..1....1..0..1..1....1..0..1..1....1..0..0..0....1..1..1..0
..0..1..1..1....1..1..0..1....1..1..1..0....1..0..0..1....1..1..1..1
..0..0..1..1....1..1..0..0....0..1..0..0....0..0..0..1....0..1..1..1

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A227259 Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having a sum of two or less, with rows and columns of the latter in lexicographically nondecreasing order.

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A227260 Number of nX3 0,1 arrays indicating 2X2 subblocks of some larger (n+1)X4 binary array having a sum of two or less, with rows and columns of the latter in lexicographically nondecreasing order.

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A227261 Number of n X 4 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 5 binary array having a sum of two or less, with rows and columns of the latter in lexicographically nondecreasing order.

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A227262 Number of nX5 0,1 arrays indicating 2X2 subblocks of some larger (n+1)X6 binary array having a sum of two or less, with rows and columns of the latter in lexicographically nondecreasing order.

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A227258 Number of n X n 0,1 arrays indicating 2X2 subblocks of some larger (n+1)X(n+1) binary array having a sum of two or less, with rows and columns of the latter in lexicographically nondecreasing order.

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