A255107 -id:A255107 - cp's OEIS frontend

A255102 Number of length n+3 0..2 arrays with at most one downstep in every 3 consecutive neighbor pairs.

66, 168, 441, 1137, 2907, 7498, 19338, 49698, 127871, 329325, 847491, 2180700, 5613144, 14447250, 37180603, 95692059, 246288681, 633868172, 1631378124, 4198705332, 10806224445, 27811942767, 71579710341, 184225016494

Offset: 1

R. H. Hardin, Feb 14 2015

nonn

Column 3 of A255107.

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

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

Cf. A255107.

Empirical: a(n) = 3*a(n-1) -3*a(n-2) +8*a(n-3) -9*a(n-4) +3*a(n-5) -a(n-6).

Empirical g.f.: x*(66 - 30*x + 135*x^2 - 210*x^3 + 69*x^4 - 26*x^5) / ((1 - x)*(1 - 2*x + x^2 - 7*x^3 + 2*x^4 - x^5)). - Colin Barker, Jan 24 2018

A255103 Number of length n+4 0..2 arrays with at most one downstep in every 4 consecutive neighbor pairs.

Original entry on oeis.org

147, 331, 789, 1905, 4429, 10125, 23463, 55246, 129480, 300432, 696375, 1623876, 3795126, 8845445, 20569653, 47880261, 111630444, 260248590, 606129714, 1411326056, 3287784315, 7661560197, 17850285244, 41578206276, 96850762992

Offset: 1

R. H. Hardin, Feb 14 2015

nonn

Column 4 of A255107.

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

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

Cf. A255107.

Empirical: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +12*a(n-4) -18*a(n-5) +7*a(n-6) -3*a(n-8) +a(n-9).

Empirical g.f.: x*(147 - 110*x + 237*x^2 + 384*x^3 - 1014*x^4 + 438*x^5 - 69*x^6 - 172*x^7 + 66*x^8) / (1 - 3*x + 3*x^2 - x^3 - 12*x^4 + 18*x^5 - 7*x^6 + 3*x^8 - x^9). - Colin Barker, Jan 24 2018

A255104 Number of length n+5 0..2 arrays with at most one downstep in every 5 consecutive neighbor pairs.

Original entry on oeis.org

294, 597, 1302, 2951, 6582, 14001, 29147, 61542, 133392, 292534, 634197, 1353282, 2874273, 6149472, 13283988, 28746325, 61881375, 132509427, 283590718, 609038592, 1311917331, 2825639015, 6072583563, 13028913003, 27962048781

Offset: 1

R. H. Hardin, Feb 14 2015

nonn

Column 5 of A255107.

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

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

Cf. A255107.

Empirical: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +18*a(n-5) -29*a(n-6) +12*a(n-7) -6*a(n-10) +3*a(n-11).

Empirical g.f.: x*(294 - 285*x + 393*x^2 + 542*x^3 + 1038*x^4 - 3486*x^5 + 1719*x^6 - 129*x^7 - 318*x^8 - 684*x^9 + 441*x^10) / (1 - 3*x + 3*x^2 - x^3 - 18*x^5 + 29*x^6 - 12*x^7 + 6*x^10 - 3*x^11). - Colin Barker, Jan 24 2018

A255105 Number of length n+6 0..2 arrays with at most one downstep in every 6 consecutive neighbor pairs.

Original entry on oeis.org

540, 1008, 2032, 4338, 9297, 19263, 38010, 73278, 143045, 288057, 594045, 1228136, 2495244, 4970793, 9823140, 19533636, 39362880, 80112560, 163010352, 329127561, 659192991, 1316427636, 2637095196, 5313657069, 10747592751, 21727946097

Offset: 1

R. H. Hardin, Feb 14 2015

nonn

Column 6 of A255107

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

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

Cf. A255107

Empirical: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +25*a(n-6) -42*a(n-7) +18*a(n-8) -10*a(n-12) +6*a(n-13)

A255106 Number of length n+7 0..2 arrays with at most one downstep in every 7 consecutive neighbor pairs.

Original entry on oeis.org

927, 1616, 3042, 6141, 12662, 25578, 49611, 91887, 166290, 303969, 573853, 1118256, 2210103, 4340001, 8343339, 15695433, 29216435, 54612816, 103548108, 199304393, 386593848, 747736983, 1432037309, 2714684340, 5119381929, 9669662693

Offset: 1

R. H. Hardin, Feb 14 2015

nonn

Column 7 of A255107

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

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

Cf. A255107

Empirical: a(n) = 3*a(n-1) -3*a(n-2) +a(n-3) +33*a(n-7) -57*a(n-8) +25*a(n-9) -15*a(n-14) +10*a(n-15)

A255108 Number of length n+1 0..2 arrays with at most one downstep in every n consecutive neighbor pairs.

Original entry on oeis.org

9, 26, 66, 147, 294, 540, 927, 1507, 2343, 3510, 5096, 7203, 9948, 13464, 17901, 23427, 30229, 38514, 48510, 60467, 74658, 91380, 110955, 133731, 160083, 190414, 225156, 264771, 309752, 360624, 417945, 482307, 554337, 634698, 724090, 823251, 932958

Offset: 1

R. H. Hardin, Feb 14 2015

nonn

Row 1 of A255107.

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

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

Cf. A255107.

Empirical: a(n) = (1/120)*n^5 + (1/6)*n^4 + (19/24)*n^3 + (11/6)*n^2 + (16/5)*n + 3.

Empirical g.f.: x*(9 - 28*x + 45*x^2 - 39*x^3 + 17*x^4 - 3*x^5) / (1 - x)^6. - Colin Barker, Jan 24 2018

A255109 Number of length n+2 0..2 arrays with at most one downstep in every n consecutive neighbor pairs.

Original entry on oeis.org

27, 75, 168, 331, 597, 1008, 1616, 2484, 3687, 5313, 7464, 10257, 13825, 18318, 23904, 30770, 39123, 49191, 61224, 75495, 92301, 111964, 134832, 161280, 191711, 226557, 266280, 311373, 362361, 419802, 484288, 556446, 636939, 726467, 825768, 935619

Offset: 1

R. H. Hardin, Feb 14 2015

nonn

Row 2 of A255107.

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

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

Cf. A255107.

Empirical: a(n) = (1/120)*n^5 + (5/24)*n^4 + (37/24)*n^3 + (175/24)*n^2 + (239/20)*n + 6.

Empirical g.f.: x*(3 - 3*x + x^2)*(9 - 20*x + 18*x^2 - 6*x^3) / (1 - x)^6. - Colin Barker, Jan 24 2018

A255110 Number of length n+3 0..2 arrays with at most one downstep in every n consecutive neighbor pairs.

Original entry on oeis.org

81, 216, 441, 789, 1302, 2032, 3042, 4407, 6215, 8568, 11583, 15393, 20148, 26016, 33184, 41859, 52269, 64664, 79317, 96525, 116610, 139920, 166830, 197743, 233091, 273336, 318971, 370521, 428544, 493632, 566412, 647547, 737737, 837720, 948273

Offset: 1

R. H. Hardin, Feb 14 2015

nonn

Row 3 of A255107.

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

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

Cf. A255107.

Empirical: a(n) = (1/120)*n^5 + (1/4)*n^4 + (59/24)*n^3 + (93/4)*n^2 + (1321/30)*n + 11.

Empirical g.f.: x*(81 - 270*x + 360*x^2 - 237*x^3 + 78*x^4 - 11*x^5) / (1 - x)^6. - Colin Barker, Jan 24 2018

A255111 Number of length n+4 0..2 arrays with at most one downstep in every n consecutive neighbor pairs.

Original entry on oeis.org

243, 622, 1137, 1905, 2951, 4338, 6141, 8448, 11361, 14997, 19489, 24987, 31659, 39692, 49293, 60690, 74133, 89895, 108273, 129589, 154191, 182454, 214781, 251604, 293385, 340617, 393825, 453567, 520435, 595056, 678093, 770246, 872253, 984891

Offset: 1

R. H. Hardin, Feb 14 2015

nonn

Row 4 of A255107.

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

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

Cf. A255107.

Empirical: a(n) = (1/120)*n^5 + (7/24)*n^4 + (85/24)*n^3 + (1505/24)*n^2 + (2809/20)*n + 30 for n>2.

Empirical g.f.: x*(243 - 836*x + 1050*x^2 - 447*x^3 - 219*x^4 + 339*x^5 - 156*x^6 + 27*x^7) / (1 - x)^6. - Colin Barker, Jan 24 2018

A255112 Number of length n+5 0..2 arrays with at most one downstep in every n consecutive neighbor pairs.

Original entry on oeis.org

729, 1791, 2907, 4429, 6582, 9297, 12662, 16779, 21765, 27753, 34893, 43353, 53320, 65001, 78624, 94439, 112719, 133761, 157887, 185445, 216810, 252385, 292602, 337923, 388841, 445881, 509601, 580593, 659484, 746937, 843652, 950367, 1067859

Offset: 1

R. H. Hardin, Feb 14 2015

nonn

Row 5 of A255107.

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

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

Cf. A255107.

Empirical: a(n) = (1/120)*n^5 + (1/3)*n^4 + (115/24)*n^3 + (889/6)*n^2 + (3867/10)*n + 111 for n>3.

Empirical g.f.: x*(729 - 2583*x + 3096*x^2 - 728*x^3 - 1272*x^4 + 591*x^5 + 618*x^6 - 594*x^7 + 144*x^8) / (1 - x)^6. - Colin Barker, Jan 24 2018

cp's OEIS Frontend

A255102 Number of length n+3 0..2 arrays with at most one downstep in every 3 consecutive neighbor pairs.

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A255103 Number of length n+4 0..2 arrays with at most one downstep in every 4 consecutive neighbor pairs.

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A255104 Number of length n+5 0..2 arrays with at most one downstep in every 5 consecutive neighbor pairs.

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A255105 Number of length n+6 0..2 arrays with at most one downstep in every 6 consecutive neighbor pairs.

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A255106 Number of length n+7 0..2 arrays with at most one downstep in every 7 consecutive neighbor pairs.

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A255108 Number of length n+1 0..2 arrays with at most one downstep in every n consecutive neighbor pairs.

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A255109 Number of length n+2 0..2 arrays with at most one downstep in every n consecutive neighbor pairs.

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A255110 Number of length n+3 0..2 arrays with at most one downstep in every n consecutive neighbor pairs.

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A255111 Number of length n+4 0..2 arrays with at most one downstep in every n consecutive neighbor pairs.

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