A240460 -id:A240460 - cp's OEIS frontend

A240456 Number of nX2 0..3 arrays with no element equal to one plus the sum of elements to its left or three plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

4, 21, 102, 476, 2200, 10123, 46471, 213000, 975380, 4464474, 20429739, 93474260, 427645941, 1956395954, 8949898045, 40942368765, 187294120155, 856787747966, 3919414321141, 17929510264717, 82019155503670, 375199231601451

Offset: 1

R. H. Hardin, Apr 05 2014

nonn

Column 2 of A240460

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

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

Empirical: a(n) = 8*a(n-1) -20*a(n-2) +34*a(n-3) -84*a(n-4) +92*a(n-5) -68*a(n-6) +222*a(n-7) +13*a(n-8) -251*a(n-9) +25*a(n-10) -495*a(n-11) +485*a(n-12) -44*a(n-13) -180*a(n-14) +554*a(n-15) -648*a(n-16) +14*a(n-17) +152*a(n-18) -190*a(n-19) -140*a(n-20) +397*a(n-21) -273*a(n-22) +75*a(n-23) +167*a(n-24) -136*a(n-25) +27*a(n-26)

A240457 Number of nX3 0..3 arrays with no element equal to one plus the sum of elements to its left or three plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

8, 89, 874, 8187, 75167, 682018, 6147372, 55212526, 494809053, 4428808128, 39611173178, 354127003547, 3165102684053, 28284608888395, 252739519980209, 2258253806476180, 20177086997089514, 180275181902738316

Offset: 1

R. H. Hardin, Apr 05 2014

nonn

Column 3 of A240460

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

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

A240458 Number of nX4 0..3 arrays with no element equal to one plus the sum of elements to its left or three plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

16, 375, 7589, 143237, 2632690, 47636104, 854671234, 15259447330, 271656519692, 4827854253348, 85712180553955, 1520764060039331, 26972330503325401, 478273812124771069, 8479592950284098842, 150327053689019608051

Offset: 1

R. H. Hardin, Apr 05 2014

nonn

Column 4 of A240460

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

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

A240459 Number of nX5 0..3 arrays with no element equal to one plus the sum of elements to its left or three plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

32, 1583, 65723, 2501883, 92193017, 3337483054, 119643524281, 4265146133201, 151546630250473, 5374173813805185, 190357922342008547, 6737907461668482163, 238393662801305197196, 8432427442592587713280, 298224063492597274075079

Offset: 1

R. H. Hardin, Apr 05 2014

nonn

Column 5 of A240460

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

R. H. Hardin, Table of n, a(n) for n = 1..181

A240461 Number of 2 X n 0..3 arrays with no element equal to one plus the sum of elements to its left or three plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

5, 21, 89, 375, 1583, 6685, 28241, 119319, 504151, 2130189, 9000729, 38030999, 160693343, 678981661, 2868918401, 12122113399, 51219871687, 216420616013, 914447487881, 3863838035639, 16325972308111, 68982542575773

Offset: 1

R. H. Hardin, Apr 05 2014

nonn

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

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

Row 2 of A240460.

Empirical: a(n) = 6*a(n-1) - 7*a(n-2) - 4*a(n-3) + 8*a(n-4).

Empirical g.f.: x*(5 - 9*x - 2*x^2 + 8*x^3) / (1 - 6*x + 7*x^2 + 4*x^3 - 8*x^4). - Colin Barker, Oct 29 2018

A240462 Number of 3Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or three plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

12, 102, 874, 7589, 65723, 568370, 4916340, 42530527, 367908385, 3182471383, 27528807013, 238127592175, 2059829147851, 17817722472564, 154124971684131, 1333195242928609, 11532260863126369, 99755106819505532, 862890740313446216

Offset: 1

R. H. Hardin, Apr 05 2014

nonn

Row 3 of A240460

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

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

Empirical: a(n) = 18*a(n-1) -105*a(n-2) +200*a(n-3) +242*a(n-4) -2119*a(n-5) +7083*a(n-6) -9004*a(n-7) -24192*a(n-8) +72426*a(n-9) -3118*a(n-10) -103236*a(n-11) -4239*a(n-12) +64281*a(n-13) +119026*a(n-14) -161710*a(n-15) +142844*a(n-16) -25892*a(n-17) -337024*a(n-18) +223288*a(n-19) +175280*a(n-20) -145120*a(n-21) -22528*a(n-22) +23040*a(n-23)

A240463 Number of 4Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or three plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

28, 476, 8187, 143237, 2501883, 43654661, 761700369, 13290291978, 231879123545, 4045526615228, 70580191049583, 1231367510496942, 21482798448261309, 374794402280678279, 6538751854554181415, 114076545131533814184

Offset: 1

R. H. Hardin, Apr 05 2014

nonn

Row 4 of A240460

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

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

A240464 Number of 5Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or three plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

66, 2200, 75167, 2632690, 92193017, 3228706651, 113105814752, 3962629938717, 138830275066900, 4863899993991019, 170406516596392953, 5970190697057475835, 209165606073684385931, 7328116621928639369238, 256740568387799086329458

Offset: 1

R. H. Hardin, Apr 05 2014

nonn

Row 5 of A240460

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

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

cp's OEIS Frontend

A240456 Number of nX2 0..3 arrays with no element equal to one plus the sum of elements to its left or three plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

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A240457 Number of nX3 0..3 arrays with no element equal to one plus the sum of elements to its left or three plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

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A240458 Number of nX4 0..3 arrays with no element equal to one plus the sum of elements to its left or three plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

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A240459 Number of nX5 0..3 arrays with no element equal to one plus the sum of elements to its left or three plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

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A240461 Number of 2 X n 0..3 arrays with no element equal to one plus the sum of elements to its left or three plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

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A240462 Number of 3Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or three plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

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A240463 Number of 4Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or three plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

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A240464 Number of 5Xn 0..3 arrays with no element equal to one plus the sum of elements to its left or three plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.

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