A269143 -id:A269143 - cp's OEIS frontend

A269137 Number of n X 2 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three no more than once.

16, 148, 1164, 8532, 59916, 408596, 2727564, 17914580, 116170764, 745617300, 4745165964, 29984668756, 188330955276, 1176750424852, 7319499656844, 45347466532308, 279961285570572, 1722988944076436, 10574188575966348

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

			Some solutions for n=4:
..2..0. .3..3. .1..0. .2..2. .3..0. .2..1. .0..0. .0..1. .3..3. .0..1
..2..2. .1..1. .1..1. .2..3. .1..0. .0..1. .0..1. .0..0. .1..1. .0..3
..3..1. .1..3. .3..1. .0..1. .0..1. .1..1. .1..1. .1..2. .1..1. .1..1
..1..1. .3..3. .0..0. .0..1. .0..0. .3..1. .0..2. .0..2. .3..0. .1..0

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

Column 2 of A269143.

Empirical: a(n) = 12*a(n-1) - 38*a(n-2) + 12*a(n-3) - a(n-4) for n>5.

Empirical g.f.: 4*x*(4 - 11*x - x^2 - x^3 + x^4) / (1 - 6*x + x^2)^2. - Colin Barker, Jan 19 2019

A269138 Number of nX3 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three no more than once.

Original entry on oeis.org

60, 1164, 18556, 275796, 3924212, 54199284, 732561916, 9740150372, 127846717716, 1660741102212, 21389485726684, 273519303765844, 3476418550368820, 43954347343683220, 553215363420258236, 6935081471870462788

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Column 3 of A269143.

			Some solutions for n=3
..3..2..2. .1..0..0. .0..0..2. .1..1..1. .3..1..0. .1..1..3. .1..3..1
..3..2..2. .2..0..2. .1..3..3. .0..3..1. .3..0..2. .3..3..3. .1..1..3
..3..3..2. .0..2..0. .3..1..1. .1..1..3. .2..0..0. .2..2..2. .1..0..1

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

Cf. A269143.

Empirical: a(n) = 26*a(n-1) -199*a(n-2) +408*a(n-3) -463*a(n-4) +322*a(n-5) -141*a(n-6) +36*a(n-7) -4*a(n-8) for n>9

A269139 Number of nX4 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three no more than once.

Original entry on oeis.org

216, 8532, 275796, 8317996, 240647068, 6766301156, 186315931804, 5049212790572, 135126561336764, 3579710280903028, 94040960852579428, 2453204481574556084, 63613980689923027716, 1641094486943583990844, 42147014968744168530996

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Column 4 of A269143.

			Some solutions for n=2
..2..3..2..2. .2..3..1..3. .0..0..1..1. .1..1..3..1. .1..1..0..1
..2..2..2..3. .3..1..1..2. .0..1..1..0. .0..1..3..3. .0..1..1..3

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

Cf. A269143.

Empirical: a(n) = 58*a(n-1) -1093*a(n-2) +7680*a(n-3) -27078*a(n-4) +58958*a(n-5) -88914*a(n-6) +82212*a(n-7) -35159*a(n-8) -20796*a(n-9) +39556*a(n-10) -11364*a(n-11) -13593*a(n-12) +9618*a(n-13) +429*a(n-14) -2060*a(n-15) +434*a(n-16) +166*a(n-17) -92*a(n-18) +16*a(n-19) -a(n-20) for n>22

A269140 Number of nX5 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three no more than once.

Original entry on oeis.org

756, 59916, 3924212, 240647068, 14197016484, 815458664276, 45920055321732, 2546667557472940, 139535357045338964, 7570570235882777884, 407418697407850105348, 21776207050517593512788, 1157149832292866826527492

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Column 5 of A269143.

			Some solutions for n=2
..0..1..3..3..3. .2..3..2..3..2. .3..1..1..3..2. .2..3..1..0..0
..1..3..2..2..3. .0..2..3..3..2. .1..0..2..3..2. .1..3..1..0..0

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

Cf. A269143.

Empirical: a(n) = 134*a(n-1) -6403*a(n-2) +137212*a(n-3) -1537987*a(n-4) +10006762*a(n-5) -41364815*a(n-6) +107588656*a(n-7) -111196320*a(n-8) -399050332*a(n-9) +2108507944*a(n-10) -4098003684*a(n-11) +445179883*a(n-12) +18009896226*a(n-13) -42207232033*a(n-14) +12581717548*a(n-15) +122544940860*a(n-16) -203283873760*a(n-17) -79843687188*a(n-18) +508551706160*a(n-19) -240288894385*a(n-20) -648319426210*a(n-21) +662670918703*a(n-22) +480938145704*a(n-23) -858808887300*a(n-24) -176689259732*a(n-25) +734283407564*a(n-26) -39751157620*a(n-27) -450104705459*a(n-28) +101139044518*a(n-29) +200718146529*a(n-30) -72282159428*a(n-31) -63674380919*a(n-32) +31546829386*a(n-33) +13183985923*a(n-34) -9057688788*a(n-35) -1275648164*a(n-36) +1571020336*a(n-37) -67398016*a(n-38) -125671104*a(n-39) +17151168*a(n-40) +3564288*a(n-41) -665856*a(n-42) for n>45

A269141 Number of nX6 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three no more than once.

Original entry on oeis.org

2592, 408596, 54199284, 6766301156, 815458664276, 95884587957284, 11067174233536260, 1259009098075800036, 141573069581490127524, 15769412440038867100180, 1742724618979587037657388

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Column 6 of A269143.

			Some solutions for n=2
..2..0..2..3..2..2. .0..2..3..1..0..0. .0..2..0..1..3..3. .1..1..1..1..1..1
..0..1..3..3..2..3. .0..2..1..1..0..0. .0..2..1..3..3..1. .0..1..3..3..1..3

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

Cf. A269143.

A269142 Number of nX7 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three no more than once.

Original entry on oeis.org

8748, 2727564, 732561916, 186315931804, 45920055321732, 11067174233536260, 2621894498331024092, 612729907775635265268, 141617828339474744759764, 32434464000726413874379876, 7371987566769862222037312812

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Column 7 of A269143.

			Some solutions for n=1
..1..3..3..1..1..3..2. .2..3..3..2..2..2..1. .2..2..3..1..0..0..2

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

Cf. A269143.

A269136 Number of n X n 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three no more than once.

Original entry on oeis.org

4, 148, 18556, 8317996, 14197016484, 95884587957284, 2621894498331024092, 294433751149574057834796, 137064853562490916405823252564, 266206369700280385363973380215109284

Offset: 1

R. H. Hardin, Feb 20 2016

nonn

Diagonal of A269143.

			Some solutions for n=3
..2..2..3. .0..0..2. .2..1..1. .2..3..2. .0..0..1. .3..1..3. .0..1..3
..3..2..3. .0..2..2. .0..0..1. .3..2..2. .1..1..3. .3..1..3. .3..1..3
..3..2..2. .0..0..1. .1..1..1. .3..2..2. .0..2..2. .3..2..3. .1..3..1

Cf. A269143.

cp's OEIS Frontend

A269137 Number of n X 2 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three no more than once.

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A269138 Number of nX3 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three no more than once.

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A269139 Number of nX4 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three no more than once.

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A269140 Number of nX5 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three no more than once.

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A269141 Number of nX6 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three no more than once.

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A269142 Number of nX7 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three no more than once.

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A269136 Number of n X n 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three no more than once.

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