A213464 -id:A213464 - cp's OEIS frontend

A213458 Number of 0..3 arrays of length n+3 with sum less than 6 in any length 4 subsequence (=less than 50% duty cycle).

106, 310, 927, 2735, 7803, 22506, 65425, 190318, 551598, 1597812, 4632940, 13439852, 38977905, 113018097, 327714656, 950345164, 2755932228, 7991769082, 23174685375, 67202984107, 194879111652, 565120621828, 1638762823886

Offset: 1

R. H. Hardin Jun 12 2012

nonn

Column 2 of A213464

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

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

Empirical: a(n) = 2*a(n-1) +a(n-2) +a(n-3) +16*a(n-4) -8*a(n-5) -13*a(n-6) -8*a(n-7) -64*a(n-8) +15*a(n-9) +37*a(n-10) +25*a(n-11) +136*a(n-12) -54*a(n-13) -36*a(n-14) -34*a(n-15) -173*a(n-16) +107*a(n-17) +19*a(n-18) +14*a(n-19) +144*a(n-20) -129*a(n-21) +4*a(n-22) +12*a(n-23) -103*a(n-24) +98*a(n-25) -18*a(n-26) -15*a(n-27) +75*a(n-28) -39*a(n-29) +18*a(n-30) +6*a(n-31) -40*a(n-32) +9*a(n-33) -8*a(n-34) -a(n-35) +11*a(n-36) -a(n-37) +a(n-38) -a(n-40)

A213459 Number of 0..3 arrays of length n+5 with sum less than 9 in any length 6 subsequence (=less than 50% duty cycle).

Original entry on oeis.org

1758, 5542, 18018, 58898, 191573, 615561, 1940673, 6155514, 19647614, 62899953, 201473363, 644672930, 2059300887, 6574540879, 20997506212, 67093545303, 214438467736, 685364105241, 2190180322534, 6998231709363, 22360737339084

Offset: 1

R. H. Hardin Jun 12 2012

nonn

Column 3 of A213464

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

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

A213460 Number of 0..3 arrays of length n+7 with sum less than 12 in any length 6 subsequence (=less than 50% duty cycle).

Original entry on oeis.org

28722, 94238, 319078, 1091036, 3737885, 12773955, 43399990, 146145812, 486196569, 1623648129, 5447568893, 18331034879, 61772986963, 208242996467, 701740238736, 2362743601059, 7947716942734, 26723699565529, 89867277897553

Offset: 1

R. H. Hardin Jun 12 2012

nonn

Column 4 of A213464

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

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

A213461 Number of 0..3 arrays of length n+9 with sum less than 15 in any length 10 subsequence (=less than 50% duty cycle).

Original entry on oeis.org

466136, 1568984, 5444644, 19105020, 67329406, 237475982, 836356119, 2935825527, 10254646515, 35582811585, 122434373801, 422379318044, 1462308785872, 5075439138225, 17643670747421, 61385086115242, 213624545918282

Offset: 1

R. H. Hardin Jun 12 2012

nonn

Column 5 of A213464

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

R. H. Hardin, Table of n, a(n) for n = 1..61

A213462 Number of 0..3 arrays of length n+11 with sum less than 18 in any length 12 subsequence (=less than 50% duty cycle).

Original entry on oeis.org

7536790, 25829770, 91147915, 325333429, 1167362677, 4198162231, 15103463125, 54284048195, 194700970891, 696196564935, 2479358418705, 8785103222513, 30936275166758, 109148631741555, 386157614218688, 1369098248146214

Offset: 1

R. H. Hardin Jun 12 2012

nonn

Column 6 of A213464

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

R. H. Hardin, Table of n, a(n) for n = 1..36

A213463 Number of 0..3 arrays of length n+13 with sum less than 21 in any length 14 subsequence (=less than 50% duty cycle).

Original entry on oeis.org

121573668, 422335348, 1508740928, 5451265872, 19808276303, 72188618371, 263422708979, 961420842175, 3506529656386, 12771245213778, 46419273790680, 168267481707156, 607940940612132, 2187698564614622, 7835295875376792

Offset: 1

R. H. Hardin Jun 12 2012

nonn

Column 7 of A213464

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

R. H. Hardin, Table of n, a(n) for n = 1..36

A213465 Number of 0..3 arrays of length 2n with sum less than 3n in any length 2n subsequence (=less than 50% duty cycle).

Original entry on oeis.org

6, 106, 1758, 28722, 466136, 7536790, 121573668, 1957953138, 31497261096, 506264941416, 8132104116670, 130559338628190, 2095252193645448, 33614011364219588, 539119053140521448, 8644670545679274098

Offset: 1

R. H. Hardin Jun 12 2012

nonn

Row 1 of A213464

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

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

A213466 Number of 0..3 arrays of length 2n+1 with sum less than 3n in any length 2n subsequence (=less than 50% duty cycle).

Original entry on oeis.org

14, 310, 5542, 94238, 1568984, 25829770, 422335348, 6874493982, 111547175144, 1805837931800, 29183975631910, 471002809679314, 7593394526409992, 122312334606560252, 1968761313647420552, 31670562474748858142

Offset: 1

R. H. Hardin Jun 12 2012

nonn

Row 2 of A213464

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

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

A213467 Number of 0..3 arrays of length 2n+2 with sum less than 3n in any length 2n subsequence (=less than 50% duty cycle).

Original entry on oeis.org

31, 927, 18018, 319078, 5444644, 91147915, 1508740928, 24791568796, 405322707108, 6602565936460, 107259549395070, 1738767957760734, 28139860212492988, 454796793295838938, 7342320714558321488

Offset: 1

R. H. Hardin Jun 12 2012

nonn

Row 3 of A213464

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

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

A213468 Number of 0..3 arrays of length 2n+3 with sum less than 3n in any length 2n subsequence (=less than 50% duty cycle).

Original entry on oeis.org

70, 2735, 58898, 1091036, 19105020, 325333429, 5451265872, 90406374528, 1488870622780, 24396922947484, 398282413965566, 6483402596528564, 105301980143117156, 1707201970861977822, 27637076220888829232

Offset: 1

R. H. Hardin Jun 12 2012

nonn

Row 4 of A213464

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

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

cp's OEIS Frontend

A213458 Number of 0..3 arrays of length n+3 with sum less than 6 in any length 4 subsequence (=less than 50% duty cycle).

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A213459 Number of 0..3 arrays of length n+5 with sum less than 9 in any length 6 subsequence (=less than 50% duty cycle).

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A213460 Number of 0..3 arrays of length n+7 with sum less than 12 in any length 6 subsequence (=less than 50% duty cycle).

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A213461 Number of 0..3 arrays of length n+9 with sum less than 15 in any length 10 subsequence (=less than 50% duty cycle).

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A213462 Number of 0..3 arrays of length n+11 with sum less than 18 in any length 12 subsequence (=less than 50% duty cycle).

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A213463 Number of 0..3 arrays of length n+13 with sum less than 21 in any length 14 subsequence (=less than 50% duty cycle).

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A213465 Number of 0..3 arrays of length 2*n with sum less than 3*n in any length 2n subsequence (=less than 50% duty cycle).

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A213466 Number of 0..3 arrays of length 2*n+1 with sum less than 3*n in any length 2n subsequence (=less than 50% duty cycle).

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A213467 Number of 0..3 arrays of length 2*n+2 with sum less than 3*n in any length 2n subsequence (=less than 50% duty cycle).

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A213468 Number of 0..3 arrays of length 2*n+3 with sum less than 3*n in any length 2n subsequence (=less than 50% duty cycle).

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A213465 Number of 0..3 arrays of length 2n with sum less than 3n in any length 2n subsequence (=less than 50% duty cycle).

A213466 Number of 0..3 arrays of length 2n+1 with sum less than 3n in any length 2n subsequence (=less than 50% duty cycle).

A213467 Number of 0..3 arrays of length 2n+2 with sum less than 3n in any length 2n subsequence (=less than 50% duty cycle).

A213468 Number of 0..3 arrays of length 2n+3 with sum less than 3n in any length 2n subsequence (=less than 50% duty cycle).