A200469 -id:A200469 - cp's OEIS frontend

A200462 Number of 0..1 arrays x(0..n-1) of n elements with each no smaller than the sum of its four previous neighbors modulo 2.

2, 3, 5, 8, 13, 20, 29, 43, 63, 91, 130, 184, 262, 370, 519, 724, 1010, 1408, 1955, 2705, 3735, 5157, 7107, 9775, 13418, 18406, 25227, 34529, 47200, 64455, 87969, 119952, 163415, 222427, 302568, 411334, 558808, 758640, 1029312, 1395882, 1891970

Offset: 1

R. H. Hardin, Nov 18 2011

nonn

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

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

Column 1 of A200469.

Configs:=  [seq(convert(16+i,base,2)[1..4],i=0..15)]:
Compatible:= proc(i,j)
 if not Configs[i][2..4]=Configs[j][1..3] then return 0 fi;
 if convert(Configs[i],`+`) mod 2 <= Configs[j][4]
 then 1 else 0
 fi
end proc:
T:= Matrix(16,16,Compatible):
initconfigs:= select(t -> t[1] <= t[2] and t[1]+t[2] mod 2 <= t[3] and t[1]+t[2]+t[3] mod 2 <= t[4], Configs):
u0:= Vector(16, i -> `if`(member(Configs[i],initconfigs),1,0)):
2,3,5,8,seq(u0^%T . T^i . e, i=1..40); # Robert Israel, Dec 11 2023

a(n) - a(n + 1) + a(n + 3) + a(n + 4) - 5*a(n + 5) + 2*a(n + 6) + 2*a(n + 7) - 2*a(n + 8) - 2*a(n + 9) + 5*a(n + 10) - a(n + 11) - 2*a(n + 12) + 2*a(n + 13) - 2*a(n + 15) + a(n + 16) = 0. - Robert Israel, Dec 11 2023

A200463 Number of 0..2 arrays x(0..n-1) of n elements with each no smaller than the sum of its four previous neighbors modulo 3.

Original entry on oeis.org

3, 6, 12, 24, 48, 98, 199, 400, 800, 1597, 3188, 6360, 12679, 25273, 50376, 100400, 200077, 398698, 794502, 1583212, 3154828, 6286514, 12526942, 24961994, 49740765, 99116372, 197505241, 393560803, 784232662, 1562708632, 3113946596, 6205036280

Offset: 1

R. H. Hardin, Nov 18 2011

nonn

Column 2 of A200469

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

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

Configs:=  [seq(convert(81+i,base,3)[1..4],i=0..80)]:
Compatible:= proc(i,j)
 if not Configs[i][2..4]=Configs[j][1..3] then return 0 fi;
 if convert(Configs[i],`+`) mod 3 <= Configs[j][4]
 then 1 else 0
 fi
end proc:
T:= Matrix(81,81,Compatible):
initconfigs:= select(t -> t[1] <= t[2] and t[1]+t[2] mod 3 <= t[3] and t[1]+t[2]+t[3] mod 3 <= t[4], Configs):
u0:= Vector(81, i -> `if`(member(Configs[i],initconfigs),1,0)):
e:= Vector(81,1):
3, 6, 12, seq(u0^%T . T^i . e, i=0..30); # Robert Israel, Dec 11 2023

a(n) - 3*a(n + 1) + 3*a(n + 2) - a(n + 3) + 2*a(n + 4) - 2*a(n + 5) - 4*a(n + 6) + 7*a(n + 7) - 2*a(n + 9) + 2*a(n + 10) - 10*a(n + 11) + 11*a(n + 12) + 3*a(n + 13) - 9*a(n + 14) + 7*a(n + 15) - 17*a(n + 16) + 22*a(n + 17) - 20*a(n + 18) + 24*a(n + 19) - 24*a(n + 20) + 13*a(n + 21) - 27*a(n + 22) + 36*a(n + 23) - 13*a(n + 24) - a(n + 25) - 11*a(n + 26) - 14*a(n + 27) + 42*a(n + 28) - 17*a(n + 29) + 9*a(n + 30) - 36*a(n + 31) + 17*a(n + 32) + 28*a(n + 33) - 19*a(n + 34) - 4*a(n + 35) + 22*a(n + 36) - 47*a(n + 37) + 82*a(n + 38) - 113*a(n + 39) + 135*a(n + 40) - 111*a(n + 41) + 45*a(n + 42) - a(n + 43) - 6*a(n + 44) + 43*a(n + 45) - 47*a(n + 46) + 17*a(n + 47) - 34*a(n + 48) + 42*a(n + 50) - 18*a(n + 51) + 10*a(n + 52) - 25*a(n + 53) + 45*a(n + 54) - 30*a(n + 55) - 18*a(n + 56) + 22*a(n + 57) - 20*a(n + 58) + 5*a(n + 59) + 27*a(n + 60) - 20*a(n + 61) + 5*a(n + 62) - 8*a(n + 63) + 23*a(n + 64) - 31*a(n + 65) + 14*a(n + 66) + 6*a(n + 67) - 24*a(n + 68) + 20*a(n + 69) + 5*a(n + 71) - 9*a(n + 72) + 3*a(n + 73) - 4*a(n + 74) - 6*a(n + 75) + 12*a(n + 76) - 4*a(n + 77) + 2*a(n + 79) - 3*a(n + 80) + a(n + 81) = 0. - Robert Israel, Dec 11 2023

A200464 Number of 0..3 arrays x(0..n-1) of n elements with each no smaller than the sum of its four previous neighbors modulo 4.

Original entry on oeis.org

4, 10, 26, 69, 181, 455, 1120, 2794, 6955, 17254, 42770, 105825, 262026, 648672, 1605786, 3974375, 9835789, 24343416, 60250311, 149117782, 369056036, 913396093, 2260628044, 5594995167, 13847440350, 34272006253, 84822308047, 209933077581

Offset: 1

R. H. Hardin Nov 18 2011

nonn

Column 3 of A200469

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

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

A200465 Number of 0..4 arrays x(0..n-1) of n elements with each no smaller than the sum of its four previous neighbors modulo 5.

Original entry on oeis.org

5, 15, 45, 135, 405, 1213, 3627, 10846, 32429, 96970, 289870, 866499, 2590128, 7742621, 23144448, 69183744, 206804024, 618180094, 1847865864, 5523643627, 16511274210, 49355507149, 147533484214, 441007079909, 1318258258809

Offset: 1

R. H. Hardin Nov 18 2011

nonn

Column 4 of A200469

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

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

A200466 Number of 0..5 arrays x(0..n-1) of n elements with each no smaller than the sum of its four previous neighbors modulo 6.

Original entry on oeis.org

6, 21, 75, 267, 951, 3328, 11576, 40309, 140298, 487872, 1695490, 5890943, 20469215, 71122969, 247110741, 858548734, 2982886197, 10363606865, 36006690099, 125099226783, 434636165827, 1510070809645, 5246488474683, 18228043608602

Offset: 1

R. H. Hardin Nov 18 2011

nonn

Column 5 of A200469

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

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

A200467 Number of 0..6 arrays x(0..n-1) of n elements with each no smaller than the sum of its four previous neighbors modulo 7.

Original entry on oeis.org

7, 28, 112, 448, 1792, 7140, 28434, 113193, 450812, 1795581, 7151892, 28486092, 113459436, 451907189, 1799936702, 7169108310, 28554377148, 113731374269, 452989138551, 1804244048124, 7186257254293, 28622677050945, 114003380196965

Offset: 1

R. H. Hardin, Nov 18 2011

nonn

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

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

Column 6 of A200469.

A200468 Number of 0..7 arrays x(0..n-1) of n elements with each no smaller than the sum of its four previous neighbors modulo 8.

Original entry on oeis.org

8, 36, 164, 750, 3434, 15446, 69136, 309748, 1386973, 6207948, 27781867, 124317636, 556310068, 2489502301, 11140314293, 49852273554, 223086037878, 998302588120, 4467360525658, 19991251154656, 89460006607948, 400329985806851

Offset: 1

R. H. Hardin Nov 18 2011

nonn

Column 7 of A200469

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

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

A200470 Number of 0..n arrays x(0..5) of 6 elements with each no smaller than the sum of its four previous neighbors modulo (n+1).

Original entry on oeis.org

20, 98, 455, 1213, 3328, 7140, 15446, 28023, 51356, 85228, 141665, 217763, 335496, 489964, 716380, 1000977, 1400376, 1894984, 2565347, 3373769, 4439204, 5709980, 7346722, 9262315, 11681488, 14491782, 17981005, 21979651, 26872568, 32446832

Offset: 1

R. H. Hardin Nov 18 2011

nonn

Row 6 of A200469

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

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

Empirical: a(n) = a(n-2) +a(n-4) -a(n-6) +3*a(n-8) -3*a(n-10) -3*a(n-12) +3*a(n-14) +2*a(n-15) -3*a(n-16) -2*a(n-17) +3*a(n-18) -2*a(n-19) +3*a(n-20) +2*a(n-21) -3*a(n-22) -6*a(n-23) +a(n-24) +6*a(n-25) -a(n-26) +6*a(n-27) -a(n-28) -6*a(n-29) +6*a(n-31) +a(n-32) -6*a(n-33) +a(n-34) -6*a(n-35) -a(n-36) +6*a(n-37) +3*a(n-38) -2*a(n-39) -3*a(n-40) +2*a(n-41) -3*a(n-42) +2*a(n-43) +3*a(n-44) -2*a(n-45) -3*a(n-46) +3*a(n-48) +3*a(n-50) -3*a(n-52) +a(n-54) -a(n-56) -a(n-58) +a(n-60)

A200471 Number of 0..n arrays x(0..6) of 7 elements with each no smaller than the sum of its four previous neighbors modulo (n+1).

Original entry on oeis.org

29, 199, 1120, 3627, 11576, 28434, 69136, 139566, 281169, 509465, 917176, 1519297, 2507652, 3907871, 6070416, 8983497, 13266213, 18901105, 26867168, 37023721, 50931188, 68369984, 91636040, 120165960, 157385059, 202502115, 260240316

Offset: 1

R. H. Hardin, Nov 18 2011

nonn

Row 7 of A200469.

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

R. H. Hardin, Table of n, a(n) for n = 1..197

Cf. A200469.

cp's OEIS Frontend

A200462 Number of 0..1 arrays x(0..n-1) of n elements with each no smaller than the sum of its four previous neighbors modulo 2.

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A200463 Number of 0..2 arrays x(0..n-1) of n elements with each no smaller than the sum of its four previous neighbors modulo 3.

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A200464 Number of 0..3 arrays x(0..n-1) of n elements with each no smaller than the sum of its four previous neighbors modulo 4.

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A200465 Number of 0..4 arrays x(0..n-1) of n elements with each no smaller than the sum of its four previous neighbors modulo 5.

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A200466 Number of 0..5 arrays x(0..n-1) of n elements with each no smaller than the sum of its four previous neighbors modulo 6.

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A200467 Number of 0..6 arrays x(0..n-1) of n elements with each no smaller than the sum of its four previous neighbors modulo 7.

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A200468 Number of 0..7 arrays x(0..n-1) of n elements with each no smaller than the sum of its four previous neighbors modulo 8.

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A200470 Number of 0..n arrays x(0..5) of 6 elements with each no smaller than the sum of its four previous neighbors modulo (n+1).

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A200471 Number of 0..n arrays x(0..6) of 7 elements with each no smaller than the sum of its four previous neighbors modulo (n+1).

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