A240192 -id:A240192 - cp's OEIS frontend

A240187 Number of n X 2 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of elements above it or three plus the sum of the elements diagonally to its northwest, modulo 4.

1, 5, 12, 27, 73, 154, 358, 872, 1871, 4438, 10338, 22880, 54100, 123711, 279854, 655190, 1491102, 3413413, 7919449, 18045604, 41514375, 95741087, 218782546, 503899032, 1158409848, 2653808377, 6109601340, 14027233372, 32187863462

Offset: 1

R. H. Hardin, Apr 02 2014

nonn

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

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

Column 2 of A240192.

Empirical: a(n) = 2*a(n-2) + 10*a(n-3) - a(n-4) - 5*a(n-5) - 15*a(n-6) + a(n-7) + 4*a(n-8) + 2*a(n-9) + 10*a(n-10) + 5*a(n-11) - 6*a(n-13).

Empirical g.f.: x*(1 + 5*x + 10*x^2 + 7*x^3 - 10*x^5 - 6*x^6 - 5*x^7 - 6*x^8 + 4*x^9 + 4*x^10 + 6*x^11) / (1 - 2*x^2 - 10*x^3 + x^4 + 5*x^5 + 15*x^6 - x^7 - 4*x^8 - 2*x^9 - 10*x^10 - 5*x^11 + 6*x^13). - Colin Barker, Oct 27 2018

A240188 Number of nX3 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of elements above it or three plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

1, 8, 37, 138, 680, 2413, 10017, 43956, 159668, 681760, 2806434, 10675575, 45462460, 181764269, 715963401, 3000804172, 11895218236, 47847647772, 197325296591, 783759057127, 3182984036915, 12972975259195, 51820141213238

Offset: 1

R. H. Hardin, Apr 02 2014

nonn

Column 3 of A240192

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

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

A240189 Number of nX4 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of elements above it or three plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

1, 14, 129, 771, 7170, 44594, 333607, 2715035, 17332017, 134735700, 1005601984, 6796746485, 52922791645, 379298005594, 2679740305873, 20445193269447, 144861185356798, 1052585343798258, 7856125918090405, 55861298280154250

Offset: 1

R. H. Hardin, Apr 02 2014

nonn

Column 4 of A240192

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

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

A240190 Number of nX5 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of elements above it or three plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

1, 26, 478, 5240, 91879, 1005029, 14022582, 206345434, 2336659626, 33576330306, 449366013476, 5493251593060, 78352851554194, 1004322433621964, 12914862745129353, 179013685774367710, 2278292415139416158

Offset: 1

R. H. Hardin, Apr 02 2014

nonn

Column 5 of A240192

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

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

A240191 Number of nX6 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of elements above it or three plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

1, 50, 1908, 40765, 1399773, 28061567, 733907809, 19388521135, 394134037392, 10503093361772, 254148197056864, 5694113978673887, 149969038048214610, 3469042519947752022, 82120588801140926261, 2085283919698276811475

Offset: 1

R. H. Hardin, Apr 02 2014

nonn

Column 6 of A240192

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

R. H. Hardin, Table of n, a(n) for n = 1..17

A240193 Number of 3 X n 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or three plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

3, 12, 37, 129, 478, 1908, 7868, 32888, 138292, 583040, 2461028, 10393720, 43907108, 185502448, 783769556, 3311604104, 13992449972, 59122342816, 249810507844, 1055529401752, 4459952527044, 18844744947024, 79625166220340

Offset: 1

R. H. Hardin, Apr 02 2014

nonn

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

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

Row 3 of A240192.

Empirical: a(n) = 9*a(n-1) - 27*a(n-2) + 29*a(n-3) + 6*a(n-4) - 32*a(n-5) + 16*a(n-6) for n>9.

Empirical g.f.: x*(3 - 15*x + 10*x^2 + 33*x^3 - 50*x^4 + 40*x^5 - 25*x^6 - 52*x^7 + 72*x^8) / ((1 - x)*(1 - 2*x)*(1 - 6*x + 7*x^2 + 4*x^3 - 8*x^4)). - Colin Barker, Oct 27 2018

A240194 Number of 4Xn 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or three plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

4, 27, 138, 771, 5240, 40765, 336257, 2843914, 24331713, 209365217, 1806459338, 15606899530, 134920604706, 1166738652794, 10090988027354, 87282067470301, 754973088693125, 6530482231898003, 56488830699787694, 488631696598081278

Offset: 1

R. H. Hardin, Apr 02 2014

nonn

Row 4 of A240192

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

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

Empirical: a(n) = 27*a(n-1) -294*a(n-2) +1660*a(n-3) -4909*a(n-4) +4008*a(n-5) +28110*a(n-6) -141830*a(n-7) +316164*a(n-8) -141103*a(n-9) -1161198*a(n-10) +2896480*a(n-11) -1515959*a(n-12) -3659154*a(n-13) +5143300*a(n-14) -13602*a(n-15) -280443*a(n-16) -7998970*a(n-17) +9853042*a(n-18) +2165540*a(n-19) -18119292*a(n-20) +21393552*a(n-21) -1551144*a(n-22) -20485792*a(n-23) +14878784*a(n-24) +4182464*a(n-25) -7981312*a(n-26) +1462784*a(n-27) +1097728*a(n-28) -368640*a(n-29) for n>34

A240195 Number of 5Xn 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or three plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

7, 73, 680, 7170, 91879, 1399773, 22849697, 385366572, 6605282704, 114179317079, 1982427469366, 34498669503396, 601074631406014, 10479195138240937, 182755667269396463, 3187784517998728377, 55609182290464067412

Offset: 1

R. H. Hardin, Apr 02 2014

nonn

Row 5 of A240192

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

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

A240196 Number of 6Xn 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or three plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

10, 154, 2413, 44594, 1005029, 28061567, 865984451, 28244997476, 950400971626, 32552155169398, 1126145490896545, 39177784539954116, 1367229766875959294, 47796738284241424246, 1672533868898522421472, 58557827201940558624795

Offset: 1

R. H. Hardin, Apr 02 2014

nonn

Row 6 of A240192

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

R. H. Hardin, Table of n, a(n) for n = 1..79

A240186 Number of n X n 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or three plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

1, 5, 37, 771, 91879, 28061567, 43398047802

Offset: 1

R. H. Hardin, Apr 02 2014

nonn

Diagonal of A240192.

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

Cf. A240192.

cp's OEIS Frontend

A240187 Number of n X 2 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of elements above it or three plus the sum of the elements diagonally to its northwest, modulo 4.

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A240188 Number of nX3 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of elements above it or three plus the sum of the elements diagonally to its northwest, modulo 4.

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A240189 Number of nX4 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of elements above it or three plus the sum of the elements diagonally to its northwest, modulo 4.

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A240190 Number of nX5 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of elements above it or three plus the sum of the elements diagonally to its northwest, modulo 4.

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A240191 Number of nX6 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of elements above it or three plus the sum of the elements diagonally to its northwest, modulo 4.

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A240193 Number of 3 X n 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or three plus the sum of the elements diagonally to its northwest, modulo 4.

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A240194 Number of 4Xn 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or three plus the sum of the elements diagonally to its northwest, modulo 4.

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A240195 Number of 5Xn 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or three plus the sum of the elements diagonally to its northwest, modulo 4.

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A240196 Number of 6Xn 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or three plus the sum of the elements diagonally to its northwest, modulo 4.

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A240186 Number of n X n 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of the elements above it or three plus the sum of the elements diagonally to its northwest, modulo 4.

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