A302278 -id:A302278 - cp's OEIS frontend

A302279 Number of 2 X n 0..1 arrays with every element equal to 1, 2 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

0, 3, 7, 10, 27, 45, 98, 193, 379, 778, 1523, 3085, 6138, 12281, 24603, 49106, 98363, 196557, 393234, 786481, 1572731, 3145946, 6291203, 12583117, 25165802, 50331369, 100663963, 201325602, 402654283, 805305613, 1610612610, 3221227041

Offset: 1

R. H. Hardin, Apr 04 2018

nonn

Row 2 of A302278.

			Some solutions for n=5:
  0 1 1 0 0     0 0 1 0 0     0 0 1 0 0     0 1 1 0 0
  1 0 0 1 1     0 1 1 0 0     0 1 1 1 0     0 0 1 1 0

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

Cf. A302278.

Empirical: a(n) = a(n-1) + 3*a(n-2) - 4*a(n-4) for n > 5.

A302274 Number of n X 4 0..1 arrays with every element equal to 1, 2 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

2, 10, 29, 89, 353, 941, 3316, 12016, 34060, 120940, 415304, 1257949, 4395268, 14710881, 46444038, 159674287, 528683443, 1709740974, 5804427370, 19154720511, 62771586925, 211230338251, 697032878924, 2300170434527, 7695594400341

Offset: 1

R. H. Hardin, Apr 04 2018

nonn

Column 4 of A302278.

			Some solutions for n=5:
  0 0 1 1     0 1 0 1     0 0 1 0     0 0 1 0     0 1 1 1
  1 0 0 1     1 0 1 0     1 1 0 1     1 1 0 0     0 0 1 0
  0 1 0 1     1 0 1 0     1 0 1 0     0 1 0 0     0 0 0 0
  0 0 1 1     0 1 0 1     1 1 1 1     0 0 1 0     1 1 0 1
  0 0 1 1     0 0 0 0     0 0 0 0     0 0 1 1     0 0 1 0

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 72

Cf. A302278.

Empirical recurrence of order 72 (see link above)

A302280 Number of 3 X n 0..1 arrays with every element equal to 1, 2 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

0, 10, 22, 29, 74, 162, 363, 782, 1766, 3953, 8784, 19606, 43887, 98136, 219234, 490655, 1098086, 2457684, 5502261, 12323540, 27604374, 61847407, 138600898, 310664178, 696450255, 1561597724, 3502013800, 7854708637, 17619975144

Offset: 1

R. H. Hardin, Apr 04 2018

nonn

Row 3 of A302278.

			Some solutions for n=5:
  0 0 1 0 0     0 0 0 1 0     0 0 1 0 0     0 1 0 1 0
  1 1 0 1 1     0 1 0 0 1     0 1 1 1 0     0 0 1 0 1
  1 0 1 0 1     1 1 0 1 1     1 0 1 0 1     0 1 1 1 1

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

Cf. A302278.

Empirical: a(n) = 4*a(n-1) -4*a(n-2) +4*a(n-3) -7*a(n-4) -17*a(n-5) +29*a(n-6) -5*a(n-7) +24*a(n-8) +6*a(n-9) -75*a(n-10) +27*a(n-11) +16*a(n-12) +7*a(n-13) -8*a(n-14) -6*a(n-15) +6*a(n-16) for n>18

A302273 Number of n X 3 0..1 arrays with every element equal to 1, 2 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 7, 22, 79, 269, 942, 3401, 12283, 43006, 156939, 565249, 2007662, 7307653, 26305407, 94096702, 341521831, 1229036517, 4413205998, 15980067713, 57514505187, 206942767678, 748087603299, 2693270343273, 9700931065070

Offset: 1

R. H. Hardin, Apr 04 2018

nonn

Column 3 of A302278.

			Some solutions for n=5:
  0 0 1    0 1 0    0 0 0    0 1 1    0 0 1    0 1 0    0 1 1
  1 1 0    0 0 1    0 1 0    0 0 1    1 1 0    1 0 1    0 0 1
  1 1 1    0 1 1    0 0 1    1 1 1    0 0 0    0 1 0    1 1 1
  1 0 0    0 0 0    1 0 0    1 1 0    1 0 0    1 0 1    0 1 1
  0 1 1    0 1 1    0 1 0    0 0 1    0 1 1    1 1 1    1 0 0

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

Cf. A302278.

Empirical: a(n) = 2*a(n-1) +5*a(n-2) +26*a(n-3) -66*a(n-4) -86*a(n-5) +79*a(n-6) +14*a(n-7) +13*a(n-8) -168*a(n-9) +250*a(n-10) +428*a(n-11) -232*a(n-12) -24*a(n-13) -160*a(n-14) +160*a(n-15) -256*a(n-16) -384*a(n-17) +256*a(n-18).

A302275 Number of n X 5 0..1 arrays with every element equal to 1, 2 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

3, 27, 74, 283, 1219, 3854, 14639, 63093, 222254, 867269, 3651231, 13909218, 55448467, 230250019, 911892066, 3685592711, 15189545391, 61267056156, 249395546907, 1024061684191, 4165273608452, 17011882082021, 69737883682027

Offset: 1

R. H. Hardin, Apr 04 2018

nonn

Column 5 of A302278.

			Some solutions for n=5:
  0 1 0 1 1     0 1 1 1 0     0 1 0 1 1     0 0 1 0 0
  1 0 1 0 0     1 0 0 0 0     1 0 0 0 0     1 1 0 1 1
  0 1 0 1 0     0 1 0 1 1     1 0 0 0 1     0 0 0 0 0
  0 0 0 0 1     0 0 0 0 0     1 1 1 1 0     1 1 0 1 1
  1 1 1 1 0     1 1 1 1 0     0 0 1 0 1     1 0 0 0 1

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

Cf. A302278.

A302276 Number of n X 6 0..1 arrays with every element equal to 1, 2 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

5, 45, 162, 649, 3621, 15862, 69601, 385242, 1809350, 8397586, 43630510, 211879132, 1010098204, 5093387513, 24992533872, 120955915176, 601661729016, 2960280723199, 14445754762414, 71411159890125, 351516742426348

Offset: 1

R. H. Hardin, Apr 04 2018

nonn

Column 6 of A302278.

			Some solutions for n=5:
  0 1 0 0 0 1     0 0 0 0 1 1     0 1 1 1 1 1     0 0 1 0 0 0
  0 0 1 1 1 0     1 1 1 1 0 0     1 0 0 0 0 0     0 1 1 0 1 0
  1 1 0 1 0 1     1 0 1 0 1 0     0 1 0 1 0 1     1 0 1 0 1 1
  0 0 0 1 0 0     1 0 0 0 1 0     1 0 0 0 1 0     1 1 1 0 0 0
  0 1 1 0 1 1     0 1 1 1 0 1     1 1 0 1 1 1     0 0 0 1 1 0

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

Cf. A302278.

A302277 Number of n X 7 0..1 arrays with every element equal to 1, 2 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

8, 98, 363, 1621, 14125, 72083, 384916, 3027442, 17837758, 105323556, 739401390, 4650704407, 28941532526, 193466816941, 1245437720868, 7947521451749, 52140138010011, 338093540539006, 2181939290185486, 14220546200647229

Offset: 1

R. H. Hardin, Apr 04 2018

nonn

Column 7 of A302278.

			Some solutions for n=5:
  0 0 1 1 1 0 0     0 0 1 0 0 0 1     0 0 1 0 1 0 0
  1 0 0 0 0 1 1     1 1 0 1 1 1 0     0 1 1 1 0 0 1
  1 1 1 0 1 0 1     1 1 1 1 1 1 1     1 0 1 0 0 1 0
  0 1 1 0 1 1 0     0 0 1 0 0 0 1     1 0 0 0 0 0 1
  0 0 1 0 0 1 1     1 1 0 1 1 1 0     1 1 0 1 1 0 0

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

Cf. A302278.

A302281 Number of 4 X n 0..1 arrays with every element equal to 1, 2 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

0, 23, 79, 89, 283, 649, 1621, 4209, 9563, 25179, 64825, 159647, 400017, 1006221, 2575287, 6472771, 16199339, 41000497, 103869515, 262156417, 659973671, 1666508525, 4216930049, 10647519701, 26860910357, 67834767395, 171448094515

Offset: 1

R. H. Hardin, Apr 04 2018

nonn

Row 4 of A302278.

			Some solutions for n=5:
  0 1 0 1 0     0 0 1 1 1     0 0 1 0 0     0 1 0 1 0
  1 0 0 0 1     1 0 0 0 0     1 1 1 0 1     1 0 1 0 1
  1 1 0 1 1     1 1 1 0 1     1 0 0 1 1     1 0 1 0 1
  1 0 1 0 1     0 0 1 1 1     1 1 0 1 1     0 1 0 1 0

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

Cf. A302278.

Empirical: a(n) = 9*a(n-1) -30*a(n-2) +46*a(n-3) -33*a(n-4) -19*a(n-5) +98*a(n-6) +116*a(n-7) -592*a(n-8) -10*a(n-9) +1664*a(n-10) -3336*a(n-11) +4033*a(n-12) -1166*a(n-13) +4404*a(n-14) -13735*a(n-15) +7376*a(n-16) +1355*a(n-17) -18717*a(n-18) +29639*a(n-19) +14401*a(n-20) +8775*a(n-21) -77658*a(n-22) +93150*a(n-23) -97491*a(n-24) -71212*a(n-25) +130345*a(n-26) +49353*a(n-27) -127543*a(n-28) +152511*a(n-29) +202885*a(n-30) -123547*a(n-31) -284655*a(n-32) -66410*a(n-33) -373017*a(n-34) -221791*a(n-35) +903034*a(n-36) +1323425*a(n-37) -122321*a(n-38) -1724187*a(n-39) -1155725*a(n-40) +507750*a(n-41) +1558721*a(n-42) +674800*a(n-43) -628203*a(n-44) -1015347*a(n-45) -246589*a(n-46) +496217*a(n-47) +496065*a(n-48) -14686*a(n-49) -252018*a(n-50) -141359*a(n-51) +56873*a(n-52) +84461*a(n-53) +12753*a(n-54) -29638*a(n-55) -11825*a(n-56) +7760*a(n-57) +6456*a(n-58) -3328*a(n-59) -3618*a(n-60) +308*a(n-61) +1056*a(n-62) +96*a(n-63) -128*a(n-64) for n>66.

A302282 Number of 5 X n 0..1 arrays with every element equal to 1, 2 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

0, 61, 269, 353, 1219, 3621, 14125, 38410, 108141, 360173, 1180191, 3638642, 10951971, 34382642, 110622932, 345400729, 1067870597, 3335600289, 10545285109, 33108634169, 103257933927, 322928627439, 1014950085156, 3186150407886

Offset: 1

R. H. Hardin, Apr 04 2018

nonn

Row 5 of A302278.

			Some solutions for n=5:
  0 1 1 0 0     0 1 1 1 1     0 1 1 1 1     0 0 1 0 0
  0 0 1 1 0     0 0 0 0 0     0 0 1 0 1     0 0 1 1 1
  0 0 0 0 0     1 1 0 1 0     0 1 0 1 1     1 1 1 0 0
  1 1 0 0 1     0 0 1 0 1     0 1 0 1 1     0 0 1 0 1
  0 0 1 1 0     0 1 0 1 0     1 0 1 0 1     0 0 1 1 1

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

Cf. A302278.

A302283 Number of 6 X n 0..1 arrays with every element equal to 1, 2 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

0, 162, 942, 941, 3854, 15862, 72083, 229708, 713848, 2948380, 12041624, 42878033, 150037123, 568430873, 2213341390, 8198208076, 29843299672, 111484320586, 422946390276, 1581927104188, 5856632633328, 21841388005545, 82061911191197

Offset: 1

R. H. Hardin, Apr 04 2018

nonn

Row 6 of A302278.

			Some solutions for n=5:
  0 1 0 1 0     0 1 1 1 0     0 1 1 1 0     0 0 1 1 1
  0 0 1 0 0     1 0 0 0 1     1 0 0 0 1     1 0 1 0 1
  1 1 0 1 1     1 0 1 0 1     0 1 0 1 0     1 1 0 0 1
  0 0 0 0 0     0 1 1 1 1     0 1 0 1 0     1 0 0 1 1
  1 1 0 1 1     1 1 0 1 0     0 0 1 0 1     1 0 1 0 1
  1 0 0 0 1     1 0 1 0 1     1 1 0 1 0     1 1 1 0 0

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

Cf. A302278.

cp's OEIS Frontend

A302279 Number of 2 X n 0..1 arrays with every element equal to 1, 2 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A302274 Number of n X 4 0..1 arrays with every element equal to 1, 2 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A302280 Number of 3 X n 0..1 arrays with every element equal to 1, 2 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A302273 Number of n X 3 0..1 arrays with every element equal to 1, 2 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A302275 Number of n X 5 0..1 arrays with every element equal to 1, 2 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A302276 Number of n X 6 0..1 arrays with every element equal to 1, 2 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A302277 Number of n X 7 0..1 arrays with every element equal to 1, 2 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A302281 Number of 4 X n 0..1 arrays with every element equal to 1, 2 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A302282 Number of 5 X n 0..1 arrays with every element equal to 1, 2 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A302283 Number of 6 X n 0..1 arrays with every element equal to 1, 2 or 4 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Views