A240284 -id:A240284 - cp's OEIS frontend

A240279 Number of nX2 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 or zero plus the sum of the elements diagonally to its northwest, modulo 4.

2, 8, 19, 38, 114, 251, 612, 1656, 3758, 9630, 24258, 57548, 146898, 360946, 880960, 2217967, 5429271, 13419200, 33424298, 82079277, 203571196, 504206276, 1242741927, 3081338174, 7616293969, 18815746878, 46600839533, 115150972966

Offset: 1

R. H. Hardin, Apr 03 2014

nonn

Column 2 of A240284

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

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

Empirical: a(n) = 3*a(n-2) +10*a(n-3) -3*a(n-4) -6*a(n-5) -3*a(n-6) +8*a(n-7) -7*a(n-8) -9*a(n-9) -4*a(n-10) +13*a(n-11) -14*a(n-12) +17*a(n-13) -a(n-15)

A240280 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 or zero plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

2, 19, 80, 262, 1461, 5443, 24490, 117962, 459193, 2147788, 9481211, 39404594, 181740410, 780110007, 3374455576, 15188622683, 65126163196, 286616870440, 1266986470030, 5476212217332, 24183642014347, 105926526183355

Offset: 1

R. H. Hardin, Apr 03 2014

nonn

Column 3 of A240284

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

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

A240281 Number of n X 4 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 or zero plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

4, 76, 570, 3457, 33183, 218658, 1851080, 15760838, 110599613, 945852472, 7409236730, 55988117579, 467427537182, 3584402597875, 28182066532013, 228525081390122, 1759513489969607, 14047642078491638, 111675119083235178

Offset: 1

R. H. Hardin, Apr 03 2014

nonn

Column 4 of A240284.

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

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

Cf. A240284.

A240282 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 or zero plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

4, 181, 2574, 28654, 484146, 5646644, 88953626, 1357879302, 17350066110, 272318368893, 3830297634073, 53008989555669, 804259922741153, 11140838537971196, 160309233474096916, 2355215686029612116

Offset: 1

R. H. Hardin, Apr 03 2014

nonn

Column 5 of A240284

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

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

A240283 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 or zero plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

8, 741, 20764, 443168, 13490093, 281488213, 8199368365, 225885684501, 5291794810655, 154532568331772, 3942966914718387, 100514669722453440, 2799309114801417209, 70561458133827649660, 1875054289432696736342

Offset: 1

R. H. Hardin, Apr 03 2014

nonn

Column 6 of A240284

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

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

A240285 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 or zero plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

2, 8, 19, 76, 181, 741, 1779, 7308, 17561, 72140, 173343, 712043, 1710905, 7027848, 16886555, 69364556, 166669597, 684625413, 1645022411, 6757226212, 16236307329, 66693560300, 160251722711, 658262849419, 1581678277825, 6497028751792

Offset: 1

R. H. Hardin, Apr 03 2014

nonn

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

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

Row 2 of A240284.

Empirical: a(n) = 12*a(n-2) - 24*a(n-4) + 31*a(n-6) - 16*a(n-8).

Empirical g.f.: x*(1 - x)*(2 + 10*x + 5*x^2 - 15*x^3 - 14*x^4 + 7*x^5 + 8*x^6) / (1 - 12*x^2 + 24*x^4 - 31*x^6 + 16*x^8). - Colin Barker, Oct 27 2018

A240286 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 or zero plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

3, 19, 80, 570, 2574, 20764, 97348, 802835, 3797188, 31467286, 149131302, 1237084277, 5865347475, 48665192186, 230756350987, 1914691579848, 9079103009997, 75334276334445, 357222415759008, 2964076274068268

Offset: 1

R. H. Hardin, Apr 03 2014

nonn

Row 3 of A240284

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

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

Empirical: a(n) = 63*a(n-2) -1109*a(n-4) +7143*a(n-6) -395*a(n-8) -201246*a(n-10) +762860*a(n-12) +347011*a(n-14) -7366154*a(n-16) +11744674*a(n-18) +3758987*a(n-20) +10095295*a(n-22) -126415852*a(n-24) +204390541*a(n-26) -65238786*a(n-28) -59211883*a(n-30) -114625640*a(n-32) +381020006*a(n-34) -342073760*a(n-36) +16725276*a(n-38) +181283664*a(n-40) -110895680*a(n-42) +16492080*a(n-44) +1175136*a(n-46) +390464*a(n-48) for n>51

A240287 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 or zero plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

4, 38, 262, 3457, 28654, 443168, 3980245, 64782938, 596789376, 9869794598, 91652276224, 1523203607042, 14179800809674, 236017741338558, 2198821491143543, 36615754869208829, 341205510217305667

Offset: 1

R. H. Hardin, Apr 03 2014

nonn

Row 4 of A240284

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

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

A240288 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 or zero plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

7, 114, 1461, 33183, 484146, 13490093, 224906182, 6988931041, 124429466670, 4051638112330, 74018226541069, 2452262844599318, 45215487411950078, 1507127744748116582, 27877553829380592951, 931147017328796104053

Offset: 1

R. H. Hardin, Apr 03 2014

nonn

Row 5 of A240284

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

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

A240289 Number of 6 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 or zero plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

10, 251, 5443, 218658, 5646644, 281488213, 8597299482, 500877279597, 17050417858056, 1080907153540112, 38722390548732389, 2543690845510555315, 92980052380043106702, 6189999145510145997607, 227935320097083755541303

Offset: 1

R. H. Hardin, Apr 03 2014

nonn

Row 6 of A240284.

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

R. H. Hardin, Table of n, a(n) for n = 1..54

Cf. A240284.

cp's OEIS Frontend

A240279 Number of nX2 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 or zero plus the sum of the elements diagonally to its northwest, modulo 4.

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A240280 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 or zero plus the sum of the elements diagonally to its northwest, modulo 4.

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A240281 Number of n X 4 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 or zero plus the sum of the elements diagonally to its northwest, modulo 4.

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A240282 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 or zero plus the sum of the elements diagonally to its northwest, modulo 4.

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A240283 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 or zero plus the sum of the elements diagonally to its northwest, modulo 4.

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A240285 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 or zero plus the sum of the elements diagonally to its northwest, modulo 4.

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A240286 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 or zero plus the sum of the elements diagonally to its northwest, modulo 4.

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A240287 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 or zero plus the sum of the elements diagonally to its northwest, modulo 4.

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A240288 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 or zero plus the sum of the elements diagonally to its northwest, modulo 4.

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A240289 Number of 6 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 or zero plus the sum of the elements diagonally to its northwest, modulo 4.

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