A301841 -id:A301841 - cp's OEIS frontend

A301842 Number of 2Xn 0..1 arrays with every element equal to 0, 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero.

2, 8, 25, 81, 263, 855, 2778, 9027, 29333, 95316, 309725, 1006437, 3270370, 10626915, 34531665, 112209036, 364618033, 1184809305, 3849982618, 12510339087, 40651763813, 132096011916, 429239834325, 1394794836717, 4532320816850

Offset: 1

R. H. Hardin, Mar 27 2018

nonn

Row 2 of A301841.

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

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

Cf. A301841.

Empirical: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4) for n>6

A301835 Number of n X n 0..1 arrays with every element equal to 0, 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

1, 8, 139, 5748, 496085, 97439921, 41966406867, 39919204098331, 84196647385137200, 391960289300558475785, 4034683591387591205214712, 91832712356420807374009031299, 4618825005074327343319160956639454

Offset: 1

R. H. Hardin, Mar 27 2018

nonn

Diagonal of A301841.

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

R. H. Hardin, Table of n, a(n) for n = 1..16

Cf. A301841.

A301836 Number of n X 3 0..1 arrays with every element equal to 0, 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

4, 25, 139, 773, 4299, 23909, 132971, 739525, 4112907, 22874149, 127215787, 707517317, 3934894923, 21884125925, 121709722091, 676895047237, 3764587553931, 20936952499621, 116441967065899, 647598149464325

Offset: 1

R. H. Hardin, Mar 27 2018

nonn

Column 3 of A301841.

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

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

Cf. A301841.

Empirical: a(n) = 7*a(n-1) -8*a(n-2) for n > 3.

A301837 Number of nX4 0..1 arrays with every element equal to 0, 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

8, 81, 678, 5748, 48802, 414385, 3518619, 29877293, 253694309, 2154171994, 18291531681, 155317282580, 1318832060857, 11198483378779, 95088702916552, 807418390272882, 6855961191710593, 58215423910060190, 494319539779559696

Offset: 1

R. H. Hardin, Mar 27 2018

nonn

Column 4 of A301841.

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

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

Cf. A301841.

Empirical: a(n) = 13*a(n-1) -46*a(n-2) +72*a(n-3) -57*a(n-4) +16*a(n-5) for n>6

A301838 Number of nX5 0..1 arrays with every element equal to 0, 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

16, 263, 3182, 39703, 496085, 6196305, 77396422, 966770632, 12076215811, 150848052398, 1884295439869, 23537397007865, 294013935342365, 3672631985528460, 45876144707506920, 573055146404781265

Offset: 1

R. H. Hardin, Mar 27 2018

nonn

Column 5 of A301841.

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

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

Cf. A301841.

Empirical: a(n) = 24*a(n-1) -201*a(n-2) +885*a(n-3) -2461*a(n-4) +4680*a(n-5) -6187*a(n-6) +5625*a(n-7) -3450*a(n-8) +1378*a(n-9) -324*a(n-10) +32*a(n-11) for n>13

A301839 Number of nX6 0..1 arrays with every element equal to 0, 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

32, 855, 15199, 281758, 5240684, 97439921, 1812097252, 33701001773, 626769301255, 11656674265408, 216791623977204, 4031908496993218, 74985787605598453, 1394592394913802694, 25936755278154522723

Offset: 1

R. H. Hardin, Mar 27 2018

nonn

Column 6 of A301841.

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

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

Cf. A301841.

Empirical: a(n) = 45*a(n-1) -812*a(n-2) +8427*a(n-3) -59225*a(n-4) +308634*a(n-5) -1256189*a(n-6) +4115169*a(n-7) -11046335*a(n-8) +24584435*a(n-9) -45781016*a(n-10) +71898912*a(n-11) -95852394*a(n-12) +108964324*a(n-13) -105845027*a(n-14) +87815455*a(n-15) -62033967*a(n-16) +37077135*a(n-17) -18559186*a(n-18) +7664773*a(n-19) -2558244*a(n-20) +670720*a(n-21) -132612*a(n-22) +18528*a(n-23) -1616*a(n-24) +64*a(n-25) for n>27

A301840 Number of nX7 0..1 arrays with every element equal to 0, 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

64, 2778, 72514, 1986213, 54948498, 1518341751, 41966406867, 1159968653556, 32062561937804, 886245421510973, 24496909108346419, 677125561489883191, 18716618615716379268, 517351460289528901541, 14300262505893118372023

Offset: 1

R. H. Hardin, Mar 27 2018

nonn

Column 7 of A301841.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 53

Cf. A301841.

Empirical recurrence of order 53 (see link above)

A301843 Number of 3Xn 0..1 arrays with every element equal to 0, 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

4, 32, 139, 678, 3182, 15199, 72514, 346244, 1653214, 7893443, 37688062, 179946317, 859175558, 4102237937, 19586633161, 93518758201, 446516665710, 2131948036306, 10179244758257, 48602040050313, 232056341426270, 1107981178164225

Offset: 1

R. H. Hardin, Mar 27 2018

nonn

Row 3 of A301841.

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

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

Cf. A301841.

Empirical: a(n) = 4*a(n-1) +3*a(n-2) +3*a(n-3) +2*a(n-4) -2*a(n-5) +2*a(n-6) -7*a(n-7) -3*a(n-8) +5*a(n-9) -4*a(n-10) -3*a(n-11) +a(n-12) for n>14

A301844 Number of 4Xn 0..1 arrays with every element equal to 0, 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

8, 128, 773, 5748, 39703, 281758, 1986213, 14047365, 99396932, 703490647, 4979239708, 35242914039, 249447707376, 1765580587312, 12496708381182, 88451201375638, 626054067443912, 4431185705002395, 31363755611152388

Offset: 1

R. H. Hardin, Mar 27 2018

nonn

Row 4 of A301841.

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

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

Cf. A301841.

Empirical: a(n) = 9*a(n-1) -11*a(n-2) -20*a(n-3) +4*a(n-4) +32*a(n-5) +164*a(n-6) -188*a(n-7) -490*a(n-8) +464*a(n-9) +542*a(n-10) -986*a(n-11) +3968*a(n-12) -8*a(n-13) -16968*a(n-14) +4086*a(n-15) +30368*a(n-16) -12378*a(n-17) -23854*a(n-18) +14224*a(n-19) +14464*a(n-20) -9340*a(n-21) -18074*a(n-22) +8682*a(n-23) +3861*a(n-24) +4655*a(n-25) -3137*a(n-26) +194*a(n-27) -1156*a(n-28) +662*a(n-29) -174*a(n-30) +60*a(n-31) -70*a(n-32) +8*a(n-33) +4*a(n-34) +4*a(n-35) for n>38

A301845 Number of 5Xn 0..1 arrays with every element equal to 0, 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

16, 512, 4299, 48802, 496085, 5240684, 54948498, 577194574, 6070236888, 63855283956, 671950959732, 7071734560895, 74426242914307, 783303529316947, 8243938456863301, 86764009232555716, 913155201853131784

Offset: 1

R. H. Hardin, Mar 27 2018

nonn

Row 5 of A301841.

			Some solutions for n=5
..0..0..0..1..1. .0..0..0..1..1. .0..0..0..0..1. .0..0..0..1..0
..1..1..0..0..1. .1..0..1..0..1. .1..1..0..1..1. .1..1..0..1..0
..1..1..1..0..1. .1..0..1..0..0. .0..1..0..1..1. .0..1..0..1..0
..0..1..0..1..0. .0..0..1..1..0. .0..1..0..1..0. .1..0..1..1..0
..0..1..0..1..1. .0..1..0..1..1. .0..1..1..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 99

Cf. A301841.

Empirical recurrence of order 99 (see link above)

cp's OEIS Frontend

A301842 Number of 2Xn 0..1 arrays with every element equal to 0, 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero.

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A301835 Number of n X n 0..1 arrays with every element equal to 0, 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero.

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A301836 Number of n X 3 0..1 arrays with every element equal to 0, 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero.

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A301837 Number of nX4 0..1 arrays with every element equal to 0, 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero.

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A301838 Number of nX5 0..1 arrays with every element equal to 0, 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero.

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A301839 Number of nX6 0..1 arrays with every element equal to 0, 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero.

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A301840 Number of nX7 0..1 arrays with every element equal to 0, 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero.

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A301843 Number of 3Xn 0..1 arrays with every element equal to 0, 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero.

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A301844 Number of 4Xn 0..1 arrays with every element equal to 0, 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero.

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