A240000 -id:A240000 - cp's OEIS frontend

A239995 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

3, 13, 61, 256, 1117, 5012, 22592, 102336, 465662, 2123857, 9698188, 44317651, 202610817, 926532786, 4237612923, 19382872561, 88661747469, 405570672096, 1855255219753, 8486814865920, 38822908166872, 177595801954595

Offset: 1

R. H. Hardin, Mar 30 2014

nonn

Column 2 of A240000

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

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)

A239996 Number of n X 3 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

4, 25, 190, 1372, 10405, 83029, 685898, 5825700, 50417154, 441675344, 3899065908, 34583504110, 307633283500, 2741312316323, 24453522555996, 218272506712305, 1949041652201113, 17407703510071602, 155496451538874916, 1389102990940616855, 12409927401794044619

Offset: 1

R. H. Hardin, Mar 30 2014

nonn

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

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

Column 3 of A240000.

A239997 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 or one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

5, 42, 526, 6527, 86360, 1225281, 18392485, 290513038, 4767970186, 80410934960, 1381071762609, 24002339457710, 420292066661594, 7394152265405038, 130463578696387397, 2306049013760669647, 40806118077181581732

Offset: 1

R. H. Hardin, Mar 30 2014

nonn

Column 4 of A240000

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

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

A239998 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

6, 65, 1262, 27415, 635873, 15981219, 429788876, 12392346376, 378942837634, 12142601105289, 402528634881777, 13658205122550505, 470581987400700236, 16373110177063830815, 573193391287239428978, 20143454978776804982736

Offset: 1

R. H. Hardin, Mar 30 2014

nonn

Column 5 of A240000

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

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

A240001 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

5, 13, 25, 42, 65, 95, 133, 180, 237, 305, 385, 478, 585, 707, 845, 1000, 1173, 1365, 1577, 1810, 2065, 2343, 2645, 2972, 3325, 3705, 4113, 4550, 5017, 5515, 6045, 6608, 7205, 7837, 8505, 9210, 9953, 10735, 11557, 12420, 13325, 14273, 15265, 16302

Offset: 1

R. H. Hardin, Mar 30 2014

nonn

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

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

Row 2 of A240000.

Empirical: a(n) = (1/6)*n^3 + 1*n^2 + (23/6)*n.
Conjectures from Colin Barker, Oct 27 2018: (Start)
G.f.: x*(5 - 7*x + 3*x^2) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
(End)

A240002 Number of 3 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

12, 61, 190, 526, 1262, 2766, 5647, 10878, 19971, 35180, 59780, 98414, 157524, 245879, 375214, 560995, 823326, 1188015, 1687817, 2363873, 3267365, 4461408, 6023201, 8046460, 10644157, 13951590, 18129810, 23369432, 29894858, 37968941

Offset: 1

R. H. Hardin, Mar 30 2014

nonn

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

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

Row 3 of A240000.

Empirical: a(n) = (1/40320)*n^8 + (1/2016)*n^7 + (7/576)*n^6 + (17/360)*n^5 + (6367/5760)*n^4 - (935/288)*n^3 + (28145/672)*n^2 - (114913/840)*n + 237 for n>6.
Conjectures from Colin Barker, Oct 27 2018: (Start)
G.f.: x*(12 - 47*x + 73*x^2 + 4*x^3 - 244*x^4 + 558*x^5 - 737*x^6 + 651*x^7 - 375*x^8 + 86*x^9 + 91*x^10 - 128*x^11 + 80*x^12 - 27*x^13 + 4*x^14) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>15.
(End)

A240003 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

28, 256, 1372, 6527, 27415, 104291, 363859, 1173141, 3539402, 10055917, 27072084, 69433880, 170442542, 402042194, 914489241, 2012051851, 4293710454, 8908363984, 18007433696, 35530979384, 68546844725, 129490989279, 239852605993

Offset: 1

R. H. Hardin, Mar 30 2014

nonn

Row 4 of A240000

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

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

Empirical: a(n) = (1/30411275102208000)*n^19 + (1/914624815104000)*n^18 + (397/2134124568576000)*n^17 + (37/62768369664000)*n^16 + (2567/6276836966400)*n^15 - (77899/8966909952000)*n^14 + (121042813/188305108992000)*n^13 - (5389171/258660864000)*n^12 + (469998043/603542016000)*n^11 - (20022197893/877879296000)*n^10 + (5869313250161/9656672256000)*n^9 - (9505177279259/689762304000)*n^8 + (12579369755410273/47076277248000)*n^7 - (3647143231803217/840647808000)*n^6 + (50430900400493621/871782912000)*n^5 - (804068701944948239/1307674368000)*n^4 + (64298607619642973/12864852000)*n^3 - (25675604169133123/882161280)*n^2 + (25119199779142691/232792560)*n - 191027452 for n>20

A240004 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

66, 1117, 10405, 86360, 635873, 4267171, 26152051, 147439332, 775122753, 3821059149, 17769229031, 78356711183, 328981383567, 1319877073978, 5076715532082, 18776009861766, 66950026301586, 230700526217982

Offset: 1

R. H. Hardin, Mar 30 2014

nonn

Row 5 of A240000

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical polynomial of degree 44

Empirical polynomial of degree 44 (see link above)

A240005 Number of 6Xn 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

156, 5012, 83029, 1225281, 15981219, 191691132, 2090236137, 20967693050, 195664738888, 1709973352188, 14072972956499, 109646306877457, 811882008990473, 5734156428747664, 38755892651094582, 251427858506122705

Offset: 1

R. H. Hardin, Mar 30 2014

nonn

Row 6 of A240000

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

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

A239994 Number of n 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

Original entry on oeis.org

2, 13, 190, 6527, 635873, 191691132, 182333502325

Offset: 1

R. H. Hardin, Mar 30 2014

Diagonal of A240000.

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

Cf. A240000.

cp's OEIS Frontend

A239995 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

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A239996 Number of n X 3 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

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A239997 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 or one plus the sum of the elements diagonally to its northwest, modulo 4.

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A239998 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

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A240001 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

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A240002 Number of 3 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

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A240003 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

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A240004 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

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A240005 Number of 6Xn 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

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A239994 Number of n 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 one plus the sum of the elements diagonally to its northwest, modulo 4.

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