A256816 -id:A256816 - cp's OEIS frontend

A256813 Number of length n+5 0..1 arrays with at most two downsteps in every 5 consecutive neighbor pairs.

63, 124, 245, 484, 956, 1888, 3728, 7362, 14539, 28712, 56701, 111974, 221128, 436688, 862380, 1703044, 3363203, 6641716, 13116185, 25902088, 51151928, 101015784, 199487860, 393952358, 777984487, 1536378320, 3034068649

Offset: 1

R. H. Hardin, Apr 10 2015

nonn

Column 5 of A256816.

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

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

Cf. A256816.

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

Empirical g.f.: x*(63 - 2*x + 60*x^2 - 8*x^3 + 48*x^4 - 32*x^5) / (1 - 2*x + x^2 - 2*x^3 + x^4 - 2*x^5 + x^6). - Colin Barker, Jan 24 2018

A256814 Number of length n+6 0..1 arrays with at most two downsteps in every 6 consecutive neighbor pairs.

Original entry on oeis.org

120, 229, 442, 856, 1656, 3204, 6192, 11955, 23088, 44617, 86226, 166620, 321960, 622104, 1202016, 2322567, 4487848, 8671757, 16756074, 32377024, 62560664, 120883084, 233577104, 451331323, 872088416, 1685098737, 3256043394

Offset: 1

R. H. Hardin, Apr 10 2015

nonn

Column 6 of A256816.

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

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

Cf. A256816.

Empirical: a(n) = 2*a(n-1) -a(n-2) +2*a(n-3) -a(n-4) +3*a(n-6) -2*a(n-7) -6*a(n-9) +4*a(n-10).

Empirical g.f.: x*(120 - 11*x + 104*x^2 - 39*x^3 + 48*x^4 + 93*x^5 - 190*x^6 - 128*x^7 - 250*x^8 + 252*x^9) / ((1 - x)*(1 - x - 2*x^3 - x^4 - x^5 - 4*x^6 - 2*x^7 - 2*x^8 + 4*x^9)). - Colin Barker, Jan 24 2018

A256815 Number of length n+7 0..1 arrays with at most two downsteps in every 7 consecutive neighbor pairs.

Original entry on oeis.org

219, 402, 753, 1424, 2693, 5088, 9613, 18104, 34013, 63928, 120362, 226816, 427341, 804974, 1516179, 2855304, 5376354, 10123582, 19065294, 35907400, 67626166, 127359488, 239852341, 451704432, 850669960, 1602023036, 3017039568

Offset: 1

R. H. Hardin, Apr 10 2015

nonn

Column 7 of A256816

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

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

Cf. A256816

Empirical: a(n) = 2*a(n-1) -a(n-2) +3*a(n-4) -2*a(n-5) +10*a(n-7) -7*a(n-8) -12*a(n-11) +9*a(n-12) -24*a(n-14) +18*a(n-15)

A256817 Number of length n+2 0..1 arrays with at most two downsteps in every n consecutive neighbor pairs.

Original entry on oeis.org

8, 16, 32, 64, 124, 229, 402, 673, 1080, 1670, 2500, 3638, 5164, 7171, 9766, 13071, 17224, 22380, 28712, 36412, 45692, 56785, 69946, 85453, 103608, 124738, 149196, 177362, 209644, 246479, 288334, 335707, 389128, 449160, 516400, 591480, 675068

Offset: 1

R. H. Hardin, Apr 10 2015

nonn

Row 2 of A256816.

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

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

Cf. A256816.

Empirical: a(n) = (1/120)*n^5 + (1/24)*n^4 + (3/8)*n^3 - (1/24)*n^2 + (277/60)*n + 3.

Empirical g.f.: x*(8 - 32*x + 56*x^2 - 48*x^3 + 20*x^4 - 3*x^5) / (1 - x)^6. - Colin Barker, Jan 21 2018

A256818 Number of length n+3 0..1 arrays with at most two downsteps in every n consecutive neighbor pairs.

Original entry on oeis.org

16, 32, 64, 128, 245, 442, 753, 1220, 1894, 2836, 4118, 5824, 8051, 10910, 14527, 19044, 24620, 31432, 39676, 49568, 61345, 75266, 91613, 110692, 132834, 158396, 187762, 221344, 259583, 302950, 351947, 407108, 469000, 538224, 615416, 701248

Offset: 1

R. H. Hardin, Apr 10 2015

nonn

Row 3 of A256816.

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

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

Cf. A256816.

Empirical: a(n) = (1/120)*n^5 + (1/12)*n^4 + (31/24)*n^3 - (31/12)*n^2 + (66/5)*n + 4.

Empirical g.f.: x*(16 - 64*x + 112*x^2 - 96*x^3 + 37*x^4 - 4*x^5) / (1 - x)^6. - Colin Barker, Jan 21 2018

A256819 Number of length n+4 0..1 arrays with at most two downsteps in every n consecutive neighbor pairs.

Original entry on oeis.org

32, 64, 128, 256, 484, 856, 1424, 2249, 3402, 4965, 7032, 9710, 13120, 17398, 22696, 29183, 37046, 46491, 57744, 71052, 86684, 104932, 126112, 150565, 178658, 210785, 247368, 288858, 335736, 388514, 447736, 513979, 587854, 670007, 761120, 861912

Offset: 1

R. H. Hardin, Apr 10 2015

nonn

Row 4 of A256816.

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

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

Cf. A256816.

Empirical: a(n) = (1/120)*n^5 + (1/8)*n^4 + (27/8)*n^3 - (65/8)*n^2 + (1897/60)*n + 3 for n>2.

Empirical g.f.: x*(32 - 128*x + 224*x^2 - 192*x^3 + 68*x^4 - 4*x^6 + x^7) / (1 - x)^6. - Colin Barker, Jan 21 2018

A256820 Number of length n+5 0..1 arrays with at most two downsteps in every n consecutive neighbor pairs.

Original entry on oeis.org

64, 128, 256, 512, 956, 1656, 2693, 4158, 6153, 8792, 12202, 16524, 21914, 28544, 36603, 46298, 57855, 71520, 87560, 106264, 127944, 152936, 181601, 214326, 251525, 293640, 341142, 394532, 454342, 521136, 595511, 678098, 769563, 870608, 981972

Offset: 1

R. H. Hardin, Apr 10 2015

nonn

Row 5 of A256816.

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

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

Cf. A256816.

Empirical: a(n) = (1/120)*n^5 + (1/6)*n^4 + (175/24)*n^3 - (103/6)*n^2 + (747/10)*n - 30 for n>3.

Empirical g.f.: x*(64 - 256*x + 448*x^2 - 384*x^3 + 124*x^4 + 16*x^5 - 7*x^6 - 8*x^7 + 4*x^8) / (1 - x)^6. - Colin Barker, Jan 21 2018

A256821 Number of length n+6 0..1 arrays with at most two downsteps in every n consecutive neighbor pairs.

Original entry on oeis.org

128, 256, 512, 1024, 1888, 3204, 5088, 7677, 11120, 15579, 21230, 28264, 36888, 47326, 59820, 74631, 92040, 112349, 135882, 162986, 194032, 229416, 269560, 314913, 365952, 423183, 487142, 558396, 637544, 725218, 822084, 928843, 1046232

Offset: 1

R. H. Hardin, Apr 10 2015

nonn

Row 6 of A256816.

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

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

Cf. A256816.

Empirical: a(n) = (1/120)*n^5 + (5/24)*n^4 + (111/8)*n^3 - (701/24)*n^2 + (11767/60)*n - 253 for n>4.

Empirical g.f.: x*(128 - 512*x + 896*x^2 - 768*x^3 + 224*x^4 + 68*x^5 - 24*x^6 - 7*x^7 - 14*x^8 + 10*x^9) / (1 - x)^6. - Colin Barker, Jan 21 2018

A256822 Number of length n+7 0..1 arrays with at most two downsteps in every n consecutive neighbor pairs.

Original entry on oeis.org

256, 512, 1024, 2048, 3728, 6192, 9613, 14168, 20075, 27566, 36888, 48304, 62094, 78556, 98007, 120784, 147245, 177770, 212762, 252648, 297880, 348936, 406321, 470568, 542239, 621926, 710252, 807872, 915474, 1033780, 1163547, 1305568

Offset: 1

R. H. Hardin, Apr 10 2015

nonn

Row 7 of A256816.

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

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

Cf. A256816.

Empirical: a(n) = (1/120)*n^5 + (1/4)*n^4 + (193/8)*n^3 - (169/4)*n^2 + (8323/15)*n - 1216 for n>5.

Empirical g.f.: x*(256 - 1024*x + 1792*x^2 - 1536*x^3 + 400*x^4 + 208*x^5 - 35*x^6 - 102*x^7 + 78*x^8 - 64*x^9 + 28*x^10) / (1 - x)^6. - Colin Barker, Jan 21 2018

cp's OEIS Frontend

A256813 Number of length n+5 0..1 arrays with at most two downsteps in every 5 consecutive neighbor pairs.

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A256814 Number of length n+6 0..1 arrays with at most two downsteps in every 6 consecutive neighbor pairs.

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A256815 Number of length n+7 0..1 arrays with at most two downsteps in every 7 consecutive neighbor pairs.

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A256817 Number of length n+2 0..1 arrays with at most two downsteps in every n consecutive neighbor pairs.

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A256818 Number of length n+3 0..1 arrays with at most two downsteps in every n consecutive neighbor pairs.

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A256819 Number of length n+4 0..1 arrays with at most two downsteps in every n consecutive neighbor pairs.

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A256820 Number of length n+5 0..1 arrays with at most two downsteps in every n consecutive neighbor pairs.

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A256821 Number of length n+6 0..1 arrays with at most two downsteps in every n consecutive neighbor pairs.

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A256822 Number of length n+7 0..1 arrays with at most two downsteps in every n consecutive neighbor pairs.

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