A240271 -id:A240271 - cp's OEIS frontend

A240266 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

4, 7, 14, 36, 72, 170, 411, 879, 2106, 4874, 10808, 25648, 58383, 132428, 310199, 704308, 1615735, 3746472, 8529529, 19647966, 45277950, 103456016, 238430432, 547803553, 1255188579, 2890336834, 6633676274, 15225374578, 35023723614

Offset: 1

R. H. Hardin, Apr 03 2014

nonn

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

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

Column 2 of A240271.

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 + x)*(4 + 3*x + 3*x^2 - 21*x^3 - x^4 - 14*x^5 + 30*x^6 - 4*x^7 + 27*x^8 - x^9 + 2*x^10 - 12*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

A240267 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

10, 35, 118, 582, 2000, 8353, 37422, 135463, 580528, 2403439, 9094559, 38858731, 155489063, 610603047, 2566277060, 10164936522, 40839681679, 168734662196, 669445744507, 2718398151862, 11090164669401, 44257273047277

Offset: 1

R. H. Hardin, Apr 03 2014

nonn

Column 3 of A240271

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

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

A240268 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

24, 157, 919, 8265, 49921, 382690, 3076452, 19781372, 154994425, 1144262410, 7794166168, 60672207307, 432430357219, 3074960725990, 23390892029200, 165455143739679, 1206985642463001, 8980338421458244, 63888419650679414

Offset: 1

R. H. Hardin, Apr 03 2014

nonn

Column 4 of A240271

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

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

A240269 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

56, 713, 7562, 126286, 1363144, 19210586, 278945445, 3200032085, 46095401280, 611757450541, 7547496685660, 107236644548985, 1371266497746832, 17737107517230511, 244729672768718950, 3116623507000444656

Offset: 1

R. H. Hardin, Apr 03 2014

nonn

Column 5 of A240271

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

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

A240270 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

132, 3263, 64721, 2059061, 40760821, 1063706501, 27923918285, 576407548906, 15326042676144, 369518944004863, 8336460134026971, 218307022801923486, 5056252479593806048, 120075470956639787034, 3035930439648129383298

Offset: 1

R. H. Hardin, Apr 03 2014

nonn

Column 6 of A240271

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

R. H. Hardin, Table of n, a(n) for n = 1..18

A240272 Number of 2Xn 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

3, 7, 35, 157, 713, 3263, 14895, 68101, 311509, 1424689, 6516312, 29807450, 136351053, 623728103, 2853225545, 13052077767, 59706884718, 273130241113, 1249440509707, 5715597380517, 26146153523610, 119606300969406

Offset: 1

R. H. Hardin, Apr 03 2014

nonn

Row 2 of A240271

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

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) for n>28

A240273 Number of 3Xn 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

4, 14, 118, 919, 7562, 64721, 563496, 4956889, 43888821, 390006208, 3473152825, 30971163817, 276395100537, 2467754655037, 22039067141607, 196858997624033, 1758568575970935, 15710437359317486, 140356344121017589

Offset: 1

R. H. Hardin, Apr 03 2014

nonn

Row 3 of A240271

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

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

A240274 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

7, 36, 582, 8265, 126286, 2059061, 34514871, 591083808, 10257888481, 179492029479, 3156570684216, 55683928149753, 984159273442563, 17414013354270353, 308343982790239450, 5462057581927992592

Offset: 1

R. H. Hardin, Apr 03 2014

nonn

Row 4 of A240271

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

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

A240275 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

10, 72, 2000, 49921, 1363144, 40760821, 1277623744, 41700264862, 1401065174093, 47967535279669, 1662365159922179, 58055815885463615, 2037231165976598098, 71699030982374305133, 2527959942776102405087, 89229063928826842973827

Offset: 1

R. H. Hardin, Apr 03 2014

nonn

Row 5 of A240271

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

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

A240276 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

15, 170, 8353, 382690, 19210586, 1063706501, 63085436203, 3958922741466, 259024497472292, 17435614748138060

Offset: 1

R. H. Hardin, Apr 03 2014

nonn

Row 6 of A240271

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

cp's OEIS Frontend

A240266 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

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A240267 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

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A240268 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

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A240269 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

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A240270 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

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A240272 Number of 2Xn 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

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A240273 Number of 3Xn 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

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A240274 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

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A240275 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

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A240276 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

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