A303421 -id:A303421 - cp's OEIS frontend

A303415 Number of n X n 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 8, 252, 30897, 14783632, 27575294129, 200493397340704, 5683010875200460450, 627998579658329070097348, 270542136528524318473547313146, 454367389836320183421616246521390670

Offset: 1

R. H. Hardin, Apr 23 2018

nonn

Diagonal of A303421.

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

R. H. Hardin, Table of n, a(n) for n = 1..12

Cf. A303421.

A303416 Number of n X 3 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

4, 32, 252, 1988, 15684, 123732, 976132, 7700788, 60752164, 479278932, 3781071812, 29829193588, 235325017444, 1856498858132, 14646075660292, 115544122910388, 911537305199524, 7191194479141332, 56731938168469572, 447563032495731188

Offset: 1

R. H. Hardin, Apr 23 2018

nonn

Column 3 of A303421.

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

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

Cf. A303421.

Empirical: a(n) = 7*a(n-1) +6*a(n-2) +8*a(n-3).

A303417 Number of nX4 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

8, 128, 1985, 30897, 480960, 7486369, 116529645, 1813851698, 28233652317, 439473157219, 6840654335738, 106478748377005, 1657403414891639, 25798444493138200, 401567736789419233, 6250634501358061189

Offset: 1

R. H. Hardin, Apr 23 2018

nonn

Column 4 of A303421.

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

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

Cf. A303421.

Empirical: a(n) = 14*a(n-1) +21*a(n-2) +54*a(n-3) -23*a(n-4) -18*a(n-5) -20*a(n-6)

A303418 Number of nX5 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

16, 512, 15647, 480953, 14783632, 454381369, 13965759339, 429248347970, 13193275586412, 405505402581780, 12463518290067297, 383075754661780748, 11774125924935072114, 361886753753857667867, 11122865797202721389960

Offset: 1

R. H. Hardin, Apr 23 2018

nonn

Column 5 of A303421.

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

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

Cf. A303421.

Empirical: a(n) = 25*a(n-1) +145*a(n-2) +920*a(n-3) +1265*a(n-4) +1083*a(n-5) -13664*a(n-6) -14525*a(n-7) -1491*a(n-8) +33615*a(n-9) +17971*a(n-10) -5436*a(n-11) -22517*a(n-12) -1311*a(n-13) +444*a(n-14) +1917*a(n-15) -144*a(n-16)

A303419 Number of nX6 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

32, 2048, 123337, 7486281, 454377792, 27575294129, 1673515027797, 101563813268522, 6163796529251277, 374074067226358827, 22702145834085172520, 1377768389855867495759, 83615256022880131226397

Offset: 1

R. H. Hardin, Apr 23 2018

nonn

Column 6 of A303421.

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

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

Cf. A303421.

Empirical: a(n) = 50*a(n-1) +537*a(n-2) +6572*a(n-3) +13015*a(n-4) -10502*a(n-5) -1034728*a(n-6) -2010884*a(n-7) +2323812*a(n-8) +37642817*a(n-9) +39027550*a(n-10) -100266124*a(n-11) -495653941*a(n-12) -186656679*a(n-13) +1174554746*a(n-14) +2832288174*a(n-15) -309318286*a(n-16) -5383405509*a(n-17) -6750919151*a(n-18) +2258857088*a(n-19) +9633134010*a(n-20) +8225359041*a(n-21) -2302191034*a(n-22) -6863063050*a(n-23) -5007931297*a(n-24) +577218190*a(n-25) +1671123600*a(n-26) +1337271024*a(n-27) +2183424*a(n-28) -35218432*a(n-29) -100046336*a(n-30) +15943680*a(n-31)

A303420 Number of nX7 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

64, 8192, 972168, 116517744, 13963574592, 1673186560760, 200493397340704, 24024569786901184, 2878797172114538576, 344958245288471965824, 41335385495979014696632, 4953104083775431293635528

Offset: 1

R. H. Hardin, Apr 23 2018

nonn

Column 7 of A303421.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 58

Cf. A303421.

Empirical recurrence of order 58 (see link above)

A303422 Number of 3Xn 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

4, 32, 252, 1985, 15647, 123337, 972168, 7662841, 60400282, 476088932, 3752642337, 29579189147, 233149966025, 1837741608616, 14485501658565, 114178052735590, 899977648952776, 7093830637396745, 55915203194889879, 440736480491065049

Offset: 1

R. H. Hardin, Apr 23 2018

nonn

Row 3 of A303421.

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

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

Cf. A303421.

Empirical: a(n) = 7*a(n-1) +4*a(n-2) +21*a(n-3) +18*a(n-4)

A303423 Number of 4Xn 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

8, 128, 1988, 30897, 480953, 7486281, 116517744, 1813509273, 28226012078, 439318146284, 6837678112091, 106423655020443, 1656409429611799, 25780849141739720, 401260805513420875, 6245342547417157374

Offset: 1

R. H. Hardin, Apr 23 2018

nonn

Row 4 of A303421.

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

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

Cf. A303421.

Empirical: a(n) = 14*a(n-1) +12*a(n-2) +175*a(n-3) +283*a(n-4) -235*a(n-5) -144*a(n-6) +67*a(n-7) -135*a(n-8) +50*a(n-9)

A303424 Number of 5Xn 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

16, 512, 15684, 480960, 14783632, 454377792, 13963574592, 429120257920, 13187561948672, 405274990273152, 12454747469604352, 382754285816985088, 11762650890909921792, 361485059270954623488, 11109013532532411652096

Offset: 1

R. H. Hardin, Apr 23 2018

nonn

Row 5 of A303421.

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

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

Cf. A303421.

Empirical: a(n) = 24*a(n-1) +128*a(n-2) +1992*a(n-3) +12020*a(n-4) +34880*a(n-5) +114640*a(n-6) -50896*a(n-7) -1751680*a(n-8) -2941888*a(n-9) +1000832*a(n-10) +4564992*a(n-11) +15197184*a(n-12) +31211520*a(n-13) +9373696*a(n-14) -4317184*a(n-15) -8290304*a(n-16) -40501248*a(n-17) -3145728*a(n-18) +16777216*a(n-19)

A303425 Number of 6 X n 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

Original entry on oeis.org

32, 2048, 123732, 7486369, 454381369, 27575294129, 1673186560760, 101524906002993, 6160343885638868, 373798050227180138, 22681348975409801485, 1376260828428633974651, 83508874354023488037997

Offset: 1

R. H. Hardin, Apr 23 2018

nonn

Row 6 of A303421.

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 44

Cf. A303421.

Empirical recurrence of order 44 (see link above).

cp's OEIS Frontend

A303415 Number of n X n 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

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A303416 Number of n X 3 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

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A303417 Number of nX4 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

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A303418 Number of nX5 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

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A303419 Number of nX6 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

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A303420 Number of nX7 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

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A303422 Number of 3Xn 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

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A303423 Number of 4Xn 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

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A303424 Number of 5Xn 0..1 arrays with every element equal to 0, 1, 2, 3, 4 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

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