A239405 -id:A239405 - cp's OEIS frontend

A239399 Number of n X 2 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of elements above it, modulo 4.

4, 23, 129, 698, 3805, 20818, 113774, 621754, 3399032, 18582965, 101593258, 555419633, 3036563927, 16601366841, 90762262155, 496211843813, 2712870511114, 14831702705726, 81087325012785, 443317575022163, 2423689199017701, 13250702601112477, 72443743963082659, 396061718589309511

Offset: 1

R. H. Hardin, Mar 17 2014

nonn

			Some solutions for n=5:
..3..1....0..0....0..3....0..0....3..3....3..3....3..3....3..1....3..1....0..0
..0..0....3..1....3..3....0..3....3..3....0..0....3..3....0..2....0..2....0..0
..2..2....2..2....3..2....0..2....3..2....2..0....2..2....0..2....0..2....0..0
..2..0....2..2....3..1....0..2....0..3....0..3....3..1....2..0....0..0....3..3
..3..2....3..1....2..0....0..0....2..0....0..2....3..1....0..0....0..2....0..0

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

Column 2 of A239405.

Empirical: a(n) = 9*a(n-1) -28*a(n-2) +74*a(n-3) -181*a(n-4) +236*a(n-5) -261*a(n-6) +234*a(n-7) +200*a(n-8) -279*a(n-9) +104*a(n-10) -268*a(n-11) -36*a(n-12) +156*a(n-13) +104*a(n-14) -32*a(n-15) -16*a(n-16).

A239400 Number of nX3 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of elements above it, modulo 4.

Original entry on oeis.org

8, 105, 1337, 16449, 205969, 2590704, 32507376, 408000104, 5124790809, 64375497505, 808627026775, 10157673828398, 127600254367522, 1602912146570029, 20135780318743491, 252946235316308314

Offset: 1

R. H. Hardin, Mar 17 2014

nonn

Column 3 of A239405

			Some solutions for n=5
..3..1..0....0..0..3....0..0..0....0..0..0....0..3..1....0..0..3....0..3..3
..3..2..0....0..0..0....0..3..1....3..3..0....3..2..1....3..1..2....3..2..3
..3..2..3....3..3..2....0..0..0....2..0..0....2..2..3....2..2..2....2..0..1
..2..2..0....2..2..0....0..3..2....0..0..3....2..2..2....2..2..3....2..2..0
..3..3..2....0..2..0....3..3..0....2..0..0....0..0..0....0..0..2....0..2..2

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 64

Empirical recurrence of order 64 (see link above)

A239401 Number of nX4 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of elements above it, modulo 4.

Original entry on oeis.org

16, 478, 13977, 394509, 11334364, 326882784, 9402398952, 270516990628, 7789048968124, 224284362847360, 6457977012007180, 185957590016422087, 5354807669541831222, 154196812648221842975, 4440254588265618959278

Offset: 1

R. H. Hardin, Mar 17 2014

nonn

Column 4 of A239405

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

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

A239402 Number of nX5 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of elements above it, modulo 4.

Original entry on oeis.org

32, 2165, 144762, 9340070, 614216271, 40566958960, 2671846338458, 176044655676921, 11610439554314901, 765805659265654829, 50509810922229600429, 3331665731491459450247, 219768507035072764751942

Offset: 1

R. H. Hardin, Mar 17 2014

nonn

Column 5 of A239405

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

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

A239403 Number of nX6 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of elements above it, modulo 4.

Original entry on oeis.org

64, 9811, 1504399, 222457036, 33522573911, 5072216819342, 765206237815409, 115478426410506313, 17442858177037612521, 2634917770699112523591, 398013557514665813580770, 60124899058707592070564461

Offset: 1

R. H. Hardin, Mar 17 2014

nonn

Column 6 of A239405

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

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

A239404 Number of nX7 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of elements above it, modulo 4.

Original entry on oeis.org

128, 44399, 15591122, 5277728354, 1820591502437, 630657074443394, 217822754771248124, 75263099558825967756, 26030827849718972763027, 9004105241933423695032678, 3114444338059091764373199789

Offset: 1

R. H. Hardin, Mar 17 2014

nonn

Column 7 of A239405

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

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

A239406 Number of 2 X n 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of the elements above it, modulo 4.

Original entry on oeis.org

5, 23, 105, 478, 2165, 9811, 44399, 201006, 909679, 4117547, 18635613, 84347726, 381758761, 1727876419, 7820451787, 35395951502, 160204196803, 725095175067, 3281826924665, 14853766696750, 67229111585533, 304283379907315

Offset: 1

R. H. Hardin, Mar 17 2014

nonn

			Some solutions for n=5:
..3..3..1..3..0....3..1..0..0..3....0..0..3..1..3....3..3..0..0..0
..0..2..0..0..0....2..0..1..1..3....3..3..2..2..2....2..0..0..1..3

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

Row 2 of A239405.

Empirical: a(n) = 3*a(n-1) + 12*a(n-2) - 18*a(n-3) - 29*a(n-4) + 19*a(n-5) + 38*a(n-6) + 8*a(n-7).

Empirical g.f.: x*(5 + 8*x - 24*x^2 - 23*x^3 + 30*x^4 + 42*x^5 + 8*x^6) / (1 - 3*x - 12*x^2 + 18*x^3 + 29*x^4 - 19*x^5 - 38*x^6 - 8*x^7). - Colin Barker, Oct 26 2018

A239407 Number of 3Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of the elements above it, modulo 4.

Original entry on oeis.org

12, 129, 1337, 13977, 144762, 1504399, 15591122, 161801518, 1677624003, 17403195529, 180479056305, 1871997954119, 19414915574725, 201369918597195, 2088509247416759, 21661501410101827, 224664541142404827

Offset: 1

R. H. Hardin, Mar 17 2014

nonn

Row 3 of A239405

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

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

Empirical: a(n) = 8*a(n-1) +73*a(n-2) -446*a(n-3) -1413*a(n-4) +8070*a(n-5) +12185*a(n-6) -63420*a(n-7) -49358*a(n-8) +220534*a(n-9) +39486*a(n-10) -241802*a(n-11) +244780*a(n-12) -89648*a(n-13) -386680*a(n-14) -228008*a(n-15) +129984*a(n-16) -457816*a(n-17) -1064416*a(n-18) -330768*a(n-19) +556128*a(n-20) -351872*a(n-21) +769280*a(n-22) +407552*a(n-23) -200704*a(n-24) +32768*a(n-25)

A239408 Number of 4Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of the elements above it, modulo 4.

Original entry on oeis.org

28, 698, 16449, 394509, 9340070, 222457036, 5277728354, 125489197292, 2979675864286, 70809806218933, 1681881988746468, 39960823740980549, 949269180927265463, 22552572727646416085, 535760871479260663596

Offset: 1

R. H. Hardin, Mar 17 2014

nonn

Row 4 of A239405

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 91

Empirical recurrence of order 91 (see link above)

A239409 Number of 5Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of the elements above it, modulo 4.

Original entry on oeis.org

66, 3805, 205969, 11334364, 614216271, 33522573911, 1820591502437, 99155297311831, 5390539057008613, 293381673332485198, 15956203146991156417, 868193383242995642964, 47226335011968154541246, 2569370658950018916786902

Offset: 1

R. H. Hardin, Mar 17 2014

nonn

Row 5 of A239405

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

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

cp's OEIS Frontend

A239399 Number of n X 2 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of elements above it, modulo 4.

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A239400 Number of nX3 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of elements above it, modulo 4.

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A239401 Number of nX4 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of elements above it, modulo 4.

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A239402 Number of nX5 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of elements above it, modulo 4.

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A239403 Number of nX6 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of elements above it, modulo 4.

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A239404 Number of nX7 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of elements above it, modulo 4.

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A239406 Number of 2 X n 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of the elements above it, modulo 4.

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A239407 Number of 3Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of the elements above it, modulo 4.

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A239408 Number of 4Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of the elements above it, modulo 4.

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A239409 Number of 5Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of the elements above it, modulo 4.

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