A200668 -id:A200668 - cp's OEIS frontend

A200661 Number of 0..1 arrays x(0..n-1) of n elements with each no smaller than the sum of its three previous neighbors modulo 2.

2, 3, 5, 8, 12, 17, 25, 36, 51, 72, 102, 144, 202, 284, 399, 560, 785, 1101, 1544, 2164, 3033, 4251, 5958, 8349, 11700, 16396, 22976, 32196, 45116, 63221, 88590, 124139, 173953, 243756, 341568, 478629, 670689, 939816, 1316935, 1845380, 2585874

Offset: 1

R. H. Hardin, Nov 20 2011

nonn

Column 1 of A200668.

			Some solutions for n=6:
..0....0....0....0....0....1....0....0....0....1....1....1....0....0....1....0
..0....0....0....0....0....1....1....1....1....1....1....1....0....1....1....0
..0....1....0....0....1....0....1....1....1....0....0....0....0....1....1....1
..1....1....1....0....1....1....0....0....0....0....1....1....0....1....1....1
..1....0....1....0....1....1....0....1....1....1....0....1....0....1....1....0
..0....1....1....1....1....1....1....0....1....1....1....0....0....1....1....0

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

Cf. A200668.

Empirical: a(n)=a(n-1)+a(n-2)-a(n-5)-a(n-6)+a(n-7).

Empirical g.f.: x*(1 + x^2)*(2 + x - 2*x^2 - x^3 + x^4) / ((1 - x)*(1 - x^2 - x^3 - x^4 + x^6)). - Colin Barker, May 21 2018

A200662 Number of 0..2 arrays x(0..n-1) of n elements with each no smaller than the sum of its three previous neighbors modulo 3.

Original entry on oeis.org

3, 6, 12, 24, 46, 89, 176, 350, 697, 1391, 2780, 5555, 11098, 22170, 44288, 88472, 176729, 353032, 705224, 1408771, 2814203, 5621746, 11230193, 22433834, 44814616, 89523251, 178834811, 357246713, 713648606, 1425609609, 2847847987, 5688961529

Offset: 1

R. H. Hardin Nov 20 2011

nonn

Column 2 of A200668

			Some solutions for n=6
..0....2....0....0....1....0....0....2....0....1....1....0....1....1....1....1
..1....2....0....0....1....0....1....2....1....2....1....0....2....1....2....2
..2....2....2....1....2....0....2....2....1....1....2....2....0....2....0....0
..0....2....2....2....1....2....0....0....2....1....2....2....2....1....1....2
..1....2....2....0....1....2....1....1....2....2....2....1....1....1....0....1
..2....0....1....2....2....2....1....0....2....2....0....2....0....1....2....2

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

Empirical: a(n) = 3*a(n-1) -3*a(n-2) +4*a(n-3) -6*a(n-4) +7*a(n-5) -9*a(n-6) +8*a(n-7) -6*a(n-8) +5*a(n-9) -4*a(n-10) +5*a(n-11) -5*a(n-12) +2*a(n-14) -3*a(n-15) +2*a(n-16) +a(n-17) -2*a(n-18) +5*a(n-19) -3*a(n-20) +a(n-21) -a(n-22) -a(n-24) +a(n-25) -a(n-26) +a(n-27)

A200663 Number of 0..3 arrays x(0..n-1) of n elements with each no smaller than the sum of its three previous neighbors modulo 4.

Original entry on oeis.org

4, 10, 26, 69, 175, 432, 1076, 2671, 6627, 16421, 40695, 100886, 250093, 619947, 1536810, 3809790, 9444489, 23412999, 58041252, 143885484, 356695266, 884255363, 2192088651, 5434237397, 13471597487, 33396394603, 82790419927, 205239329905

Offset: 1

R. H. Hardin Nov 20 2011

nonn

Column 3 of A200668

			Some solutions for n=6
..0....2....0....1....1....2....3....1....1....1....2....2....0....1....0....2
..3....3....2....1....1....2....3....3....3....1....2....3....2....3....3....2
..3....3....2....3....2....0....3....0....0....2....3....3....2....1....3....0
..2....2....1....2....1....2....2....1....2....3....3....3....1....1....3....3
..3....0....1....3....3....3....3....1....2....3....0....2....1....1....2....1
..1....2....3....2....2....3....3....3....2....1....3....1....2....3....1....1

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

Empirical: a(n) = 3*a(n-1) -a(n-3) -6*a(n-4) -2*a(n-5) +4*a(n-6) +10*a(n-7) +8*a(n-8) -4*a(n-9) -37*a(n-10) +12*a(n-11) +5*a(n-12) +27*a(n-13) +6*a(n-14) -10*a(n-15) -25*a(n-16) -a(n-17) +23*a(n-19) -7*a(n-20) -14*a(n-21) -9*a(n-22) +94*a(n-23) -90*a(n-24) -38*a(n-25) +88*a(n-26) -72*a(n-27) +64*a(n-28) +75*a(n-29) -94*a(n-30) -141*a(n-31) +114*a(n-32) +23*a(n-33) +71*a(n-34) -49*a(n-35) -58*a(n-36) -100*a(n-37) +48*a(n-38) +140*a(n-39) -56*a(n-40) +32*a(n-41) -43*a(n-42) +18*a(n-43) +6*a(n-44) -14*a(n-45) -10*a(n-46) -12*a(n-47) +27*a(n-48) -2*a(n-49) -4*a(n-50) +6*a(n-51) -6*a(n-52) -2*a(n-53) +3*a(n-54) +3*a(n-55) -2*a(n-56) -a(n-57) +5*a(n-58) -5*a(n-59) +2*a(n-63) -a(n-64)

A200664 Number of 0..4 arrays x(0..n-1) of n elements with each no smaller than the sum of its three previous neighbors modulo 5.

Original entry on oeis.org

5, 15, 45, 135, 406, 1217, 3650, 10959, 32941, 99044, 297812, 895494, 2692703, 8096855, 24346869, 73209872, 220138513, 661945308, 1990435887, 5985139586, 17997009753, 54116091662, 162724331983, 489303778636, 1471311543936

Offset: 1

R. H. Hardin Nov 20 2011

nonn

Column 4 of A200668

			Some solutions for n=6
..1....0....2....1....2....3....0....1....2....3....1....0....0....0....1....0
..4....1....3....3....3....4....0....2....3....4....4....4....0....1....2....1
..1....3....3....4....1....4....0....3....1....3....4....4....0....4....4....2
..3....4....4....3....2....2....0....2....2....3....4....4....3....2....2....3
..4....4....0....3....1....0....1....4....2....1....2....4....4....4....4....2
..4....1....2....2....4....4....2....4....0....2....2....3....3....4....3....2

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

A200666 Number of 0..6 arrays x(0..n-1) of n elements with each no smaller than the sum of its three previous neighbors modulo 7.

Original entry on oeis.org

7, 28, 112, 448, 1813, 7322, 29536, 119066, 479993, 1935168, 7802161, 31456852, 126827111, 511338342, 2061602939, 8311924900, 33511832745, 135112262286, 544742594039, 2196280995578, 8854916583356, 35701054472646, 143938712300001

Offset: 1

R. H. Hardin, Nov 20 2011

nonn

			Some solutions for n=6:
..1....3....1....4....0....4....4....2....5....4....1....2....1....4....0....2
..6....4....3....6....4....6....4....5....5....6....1....3....4....6....0....5
..1....4....4....3....5....3....4....1....5....4....5....6....6....4....3....0
..6....6....2....6....5....6....6....1....4....0....4....5....4....6....6....4
..6....6....2....1....6....5....4....4....6....5....6....5....0....5....2....6
..6....3....5....5....2....1....5....6....6....5....6....5....5....6....5....6

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

Column 6 of A200668.

A200667 Number of 0..7 arrays x(0..n-1) of n elements with each no smaller than the sum of its three previous neighbors modulo 8.

Original entry on oeis.org

8, 36, 164, 750, 3414, 15504, 70412, 319532, 1449895, 6578528, 29850070, 135443522, 614568094, 2788573700, 12653014693, 57412388798, 260505742646, 1182031264628, 5363405068469, 24336170423291, 110424101519685, 501043586283665

Offset: 1

R. H. Hardin Nov 20 2011

nonn

Column 7 of A200668

			Some solutions for n=6
..4....4....2....5....3....0....1....1....4....4....0....0....0....6....0....0
..6....4....6....7....7....0....7....3....5....5....4....5....3....7....4....0
..6....3....0....4....6....1....7....5....2....5....5....5....6....5....4....3
..4....4....6....5....3....1....7....4....4....6....7....6....1....4....1....7
..2....5....6....0....7....4....6....7....3....0....6....2....6....0....4....4
..5....5....5....1....4....6....7....5....5....7....6....7....6....7....2....6

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

A200669 Number of 0..n arrays x(0..4) of 5 elements with each no smaller than the sum of its three previous neighbors modulo (n+1).

Original entry on oeis.org

12, 46, 175, 406, 938, 1813, 3414, 5682, 9412, 14443, 22009, 31668, 45374, 62393, 85516, 113373, 149874, 193249, 248539, 312886, 393096, 485530, 598634, 727155, 881972, 1056600, 1264221, 1495936, 1768186, 2070552, 2422168, 2809532, 3256044

Offset: 1

R. H. Hardin Nov 20 2011

nonn

Row 5 of A200668

			Some solutions for n=6
..5....0....5....1....1....4....4....0....4....0....0....4....0....0....1....4
..5....3....5....1....2....6....5....1....5....5....4....6....3....1....6....5
..4....5....5....6....5....4....6....6....5....6....4....4....6....6....0....5
..6....6....1....2....5....5....3....1....1....4....2....0....6....2....1....0
..5....1....4....5....5....4....2....4....4....2....3....4....1....3....6....4

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

Empirical: a(n) = -2*a(n-1) -2*a(n-2) +5*a(n-4) +8*a(n-5) +7*a(n-6) +2*a(n-7) -5*a(n-8) -8*a(n-9) -9*a(n-10) -10*a(n-11) -9*a(n-12) -6*a(n-13) +4*a(n-14) +16*a(n-15) +20*a(n-16) +16*a(n-17) +4*a(n-18) -6*a(n-19) -9*a(n-20) -10*a(n-21) -9*a(n-22) -8*a(n-23) -5*a(n-24) +2*a(n-25) +7*a(n-26) +8*a(n-27) +5*a(n-28) -2*a(n-30) -2*a(n-31) -a(n-32)

A200670 Number of 0..n arrays x(0..5) of 6 elements with each no smaller than the sum of its three previous neighbors modulo (n+1).

Original entry on oeis.org

17, 89, 432, 1217, 3283, 7322, 15504, 28743, 52389, 87890, 145070, 225134, 345639, 507376, 738960, 1038003, 1448418, 1966975, 2656248, 3504620, 4603324, 5934897, 7622356, 9631810, 12132029, 15075684, 18682566, 22873460, 27937667, 33775988

Offset: 1

R. H. Hardin Nov 20 2011

nonn

Row 6 of A200668

			Some solutions for n=6
..5....3....1....1....3....0....0....1....2....1....0....4....0....0....2....1
..5....6....6....1....4....3....4....1....5....3....1....4....3....2....3....2
..6....3....4....6....2....6....5....6....1....4....6....5....6....3....5....3
..5....6....6....4....3....2....5....6....4....4....0....6....6....6....4....6
..6....5....4....4....3....6....0....6....5....6....0....5....6....5....5....5
..3....3....1....3....2....5....4....5....6....6....6....2....6....4....1....6

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

Empirical: a(n) = -4*a(n-1) -11*a(n-2) -23*a(n-3) -40*a(n-4) -59*a(n-5) -74*a(n-6) -75*a(n-7) -50*a(n-8) +11*a(n-9) +112*a(n-10) +244*a(n-11) +385*a(n-12) +497*a(n-13) +536*a(n-14) +458*a(n-15) +238*a(n-16) -121*a(n-17) -575*a(n-18) -1044*a(n-19) -1421*a(n-20) -1595*a(n-21) -1481*a(n-22) -1044*a(n-23) -322*a(n-24) +578*a(n-25) +1489*a(n-26) +2226*a(n-27) +2618*a(n-28) +2560*a(n-29) +2034*a(n-30) +1125*a(n-31) -1125*a(n-33) -2034*a(n-34) -2560*a(n-35) -2618*a(n-36) -2226*a(n-37) -1489*a(n-38) -578*a(n-39) +322*a(n-40) +1044*a(n-41) +1481*a(n-42) +1595*a(n-43) +1421*a(n-44) +1044*a(n-45) +575*a(n-46) +121*a(n-47) -238*a(n-48) -458*a(n-49) -536*a(n-50) -497*a(n-51) -385*a(n-52) -244*a(n-53) -112*a(n-54) -11*a(n-55) +50*a(n-56) +75*a(n-57) +74*a(n-58) +59*a(n-59) +40*a(n-60) +23*a(n-61) +11*a(n-62) +4*a(n-63) +a(n-64)

A200671 Number of 0..n arrays x(0..6) of 7 elements with each no smaller than the sum of its three previous neighbors modulo (n+1).

Original entry on oeis.org

25, 176, 1076, 3650, 11516, 29536, 70412, 145431, 291683, 534853, 956522, 1600651, 2633406, 4126715, 6386960, 9505210, 14002011, 20025031, 28396896, 39265235, 53923628, 72565437, 97086596, 127619975, 166939721, 215170884, 276186538

Offset: 1

R. H. Hardin Nov 20 2011

nonn

Row 7 of A200668

			Some solutions for n=6
..1....0....0....3....1....0....0....5....0....1....1....2....5....2....5....1
..6....1....1....4....1....2....1....6....2....6....6....5....5....5....5....6
..4....3....1....1....5....6....2....5....6....4....5....3....5....2....5....0
..5....6....2....6....1....6....4....4....6....5....5....3....5....5....5....5
..5....6....6....4....4....3....2....5....0....4....4....4....4....6....1....4
..6....2....6....5....4....6....1....6....6....6....5....4....5....6....5....6
..2....5....1....4....4....4....1....3....6....6....3....5....2....6....6....2

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

A200665 Number of 0..5 arrays x(0..n-1) of n elements with each no smaller than the sum of its three previous neighbors modulo 6.

Original entry on oeis.org

6, 21, 75, 267, 938, 3283, 11516, 40399, 141745, 497298, 1744684, 6121152, 21475315, 75342932, 264330011, 927363850, 3253519870, 11414498822, 40046099291, 140495874086, 492909198404, 1729299730308, 6066994825927, 21285162746386

Offset: 1

R. H. Hardin Nov 20 2011

nonn

Column 5 of A200668

			Some solutions for n=6
..0....2....3....0....3....4....1....1....2....0....2....4....0....1....0....1
..3....4....3....0....5....5....5....4....2....3....2....5....1....3....1....2
..3....1....0....0....5....3....2....5....5....5....5....4....5....5....5....3
..1....2....5....0....3....4....5....4....5....4....3....2....1....4....3....3
..2....5....3....0....4....3....4....4....4....5....4....5....2....3....4....3
..5....3....3....4....4....4....5....3....4....4....0....5....2....1....4....3

cp's OEIS Frontend

A200661 Number of 0..1 arrays x(0..n-1) of n elements with each no smaller than the sum of its three previous neighbors modulo 2.

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A200662 Number of 0..2 arrays x(0..n-1) of n elements with each no smaller than the sum of its three previous neighbors modulo 3.

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A200663 Number of 0..3 arrays x(0..n-1) of n elements with each no smaller than the sum of its three previous neighbors modulo 4.

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A200664 Number of 0..4 arrays x(0..n-1) of n elements with each no smaller than the sum of its three previous neighbors modulo 5.

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A200666 Number of 0..6 arrays x(0..n-1) of n elements with each no smaller than the sum of its three previous neighbors modulo 7.

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A200667 Number of 0..7 arrays x(0..n-1) of n elements with each no smaller than the sum of its three previous neighbors modulo 8.

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A200669 Number of 0..n arrays x(0..4) of 5 elements with each no smaller than the sum of its three previous neighbors modulo (n+1).

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A200670 Number of 0..n arrays x(0..5) of 6 elements with each no smaller than the sum of its three previous neighbors modulo (n+1).

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A200671 Number of 0..n arrays x(0..6) of 7 elements with each no smaller than the sum of its three previous neighbors modulo (n+1).

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A200665 Number of 0..5 arrays x(0..n-1) of n elements with each no smaller than the sum of its three previous neighbors modulo 6.

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