A255992 -id:A255992 - cp's OEIS frontend

A255993 Number of length n+2 0..1 arrays with at most one downstep in every n consecutive neighbor pairs.

8, 16, 28, 45, 68, 98, 136, 183, 240, 308, 388, 481, 588, 710, 848, 1003, 1176, 1368, 1580, 1813, 2068, 2346, 2648, 2975, 3328, 3708, 4116, 4553, 5020, 5518, 6048, 6611, 7208, 7840, 8508, 9213, 9956, 10738, 11560, 12423, 13328, 14276, 15268, 16305

Offset: 1

R. H. Hardin, Mar 13 2015

nonn

Row 2 of A255992.

Let T(n,k) = n*k + binomial(k+n, n+1), then A001477 (n=0), A000096 (n=1), and presumably this sequence (n=2). Seen this way a(0)=0, a(1)=3 and the offset here should be 2 (as is also hinted by the name: "Number of length n+2 .."). - Peter Luschny, Aug 25 2019

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

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

Cf. A255992.

Empirical: a(n) = (1/6)*n^3 + n^2 + (23/6)*n + 3.
Empirical g.f.: x*(2 - x)*(4 - 6*x + 3*x^2) / (1 - x)^4. - Colin Barker, Jan 25 2018
Empirical: a(n) = A000292(n+3) - A000124(n+1). - Torlach Rush, Aug 04 2018

A255988 Number of length n+4 0..1 arrays with at most one downstep in every 4 consecutive neighbor pairs.

Original entry on oeis.org

26, 45, 80, 144, 256, 451, 796, 1413, 2510, 4448, 7872, 13943, 24718, 43817, 77636, 137540, 243712, 431899, 765360, 1356169, 2403034, 4258172, 7545592, 13370799, 23692770, 41983189, 74394040, 131826104, 233594880, 413927683, 733476228

Offset: 1

R. H. Hardin, Mar 13 2015

nonn

Column 4 of A255992.

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

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

Cf. A255992.

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

Empirical g.f.: x*(26 - 7*x + 16*x^2 + 29*x^3 - 30*x^4) / (1 - 2*x + x^2 - 3*x^4 + 2*x^5). - Colin Barker, Jan 24 2018

A255989 Number of length n+5 0..1 arrays with at most one downstep in every 5 consecutive neighbor pairs.

Original entry on oeis.org

42, 68, 114, 196, 337, 568, 945, 1574, 2645, 4476, 7568, 12736, 21365, 35852, 60308, 101608, 171148, 287940, 484045, 813826, 1369115, 2304172, 3877545, 6523278, 10972180, 18456064, 31049291, 52240182, 87891550, 147861804, 248739774

Offset: 1

R. H. Hardin, Mar 13 2015

nonn

Column 5 of A255992.

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

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

Cf. A255992.

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

Empirical g.f.: x*(42 - 16*x + 20*x^2 + 36*x^3 + 59*x^4 - 78*x^5) / ((1 + x - x^3)*(1 - 3*x + 4*x^2 - 3*x^3)). - Colin Barker, Jan 24 2018

A255990 Number of length n+6 0..1 arrays with at most one downstep in every 6 consecutive neighbor pairs.

Original entry on oeis.org

64, 98, 156, 257, 428, 705, 1134, 1797, 2848, 4560, 7384, 12021, 19508, 31444, 50432, 80828, 129904, 209549, 338650, 546939, 881612, 1418697, 2281990, 3673412, 5919888, 9546459, 15393334, 24807246, 39956320, 64344494, 103638460, 166985169

Offset: 1

R. H. Hardin, Mar 13 2015

nonn

Column 6 of A255992.

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

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

Cf. A255992.

Empirical: a(n) = 2*a(n-1) -a(n-2) +5*a(n-6) -4*a(n-7).

Empirical g.f.: x*(64 - 30*x + 24*x^2 + 43*x^3 + 70*x^4 + 106*x^5 - 168*x^6) / (1 - 2*x + x^2 - 5*x^6 + 4*x^7). - Colin Barker, Jan 24 2018

A255991 Number of length n+7 0..1 arrays with at most one downstep in every 7 consecutive neighbor pairs.

Original entry on oeis.org

93, 136, 207, 328, 530, 854, 1352, 2088, 3175, 4824, 7406, 11528, 18124, 28562, 44768, 69584, 107469, 165670, 256009, 397452, 619647, 967640, 1509297, 2347848, 3643074, 5646004, 8753601, 13591820, 21137644, 32901050, 51205059, 79628272, 123712139

Offset: 1

R. H. Hardin, Mar 13 2015

nonn

Column 7 of A255992.

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

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

Cf. A255992.

Empirical: a(n) = 2*a(n-1) -a(n-2) +6*a(n-7) -5*a(n-8).

Empirical g.f.: x*(93 - 50*x + 28*x^2 + 50*x^3 + 81*x^4 + 122*x^5 + 174*x^6 - 320*x^7) / (1 - 2*x + x^2 - 6*x^7 + 5*x^8). - Colin Barker, Jan 25 2018

A255994 Number of length n+3 0..1 arrays with at most one downstep in every n consecutive neighbor pairs.

Original entry on oeis.org

16, 32, 53, 80, 114, 156, 207, 268, 340, 424, 521, 632, 758, 900, 1059, 1236, 1432, 1648, 1885, 2144, 2426, 2732, 3063, 3420, 3804, 4216, 4657, 5128, 5630, 6164, 6731, 7332, 7968, 8640, 9349, 10096, 10882, 11708, 12575, 13484, 14436, 15432, 16473, 17560

Offset: 1

R. H. Hardin, Mar 13 2015

nonn

Row 3 of A255992.

			Some solutions for n=4:
..0....1....0....0....1....0....1....0....1....1....0....0....1....1....0....0
..1....1....0....0....1....1....1....0....0....1....1....1....1....0....1....0
..0....0....0....0....1....0....0....1....0....1....1....1....1....1....0....1
..1....0....1....1....0....0....0....1....0....1....1....0....0....1....0....1
..1....0....0....0....0....0....1....1....0....1....0....0....0....1....0....0
..1....0....0....0....1....0....1....0....1....1....0....0....0....1....1....0
..1....0....1....0....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. A255992.

Empirical: a(n) = (1/6)*n^3 + (3/2)*n^2 + (31/3)*n + 4.

Empirical g.f.: x*(16 - 32*x + 21*x^2 - 4*x^3) / (1 - x)^4. - Colin Barker, Jan 25 2018

A255995 Number of length n+4 0..1 arrays with at most one downstep in every n consecutive neighbor pairs.

Original entry on oeis.org

32, 64, 100, 144, 196, 257, 328, 410, 504, 611, 732, 868, 1020, 1189, 1376, 1582, 1808, 2055, 2324, 2616, 2932, 3273, 3640, 4034, 4456, 4907, 5388, 5900, 6444, 7021, 7632, 8278, 8960, 9679, 10436, 11232, 12068, 12945, 13864, 14826, 15832, 16883, 17980

Offset: 1

R. H. Hardin, Mar 13 2015

nonn

Row 4 of A255992.

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

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

Cf. A255992.

Empirical: a(n) = (1/6)*n^3 + 2*n^2 + (143/6)*n + 6 for n>2.

Empirical g.f.: x*(32 - 64*x + 36*x^2 - 4*x^4 + x^5) / (1 - x)^4. - Colin Barker, Jan 25 2018

A255996 Number of length n+5 0..1 arrays with at most one downstep in every n consecutive neighbor pairs.

Original entry on oeis.org

64, 128, 188, 256, 337, 428, 530, 644, 771, 912, 1068, 1240, 1429, 1636, 1862, 2108, 2375, 2664, 2976, 3312, 3673, 4060, 4474, 4916, 5387, 5888, 6420, 6984, 7581, 8212, 8878, 9580, 10319, 11096, 11912, 12768, 13665, 14604, 15586, 16612, 17683, 18800

Offset: 1

R. H. Hardin, Mar 13 2015

nonn

Row 5 of A255992.

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

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

Cf. A255992.

Empirical: a(n) = (1/6)*n^3 + (5/2)*n^2 + (145/3)*n + 12 for n>3.

Empirical g.f.: x*(64 - 128*x + 60*x^2 + 16*x^3 - 7*x^4 - 8*x^5 + 4*x^6) / (1 - x)^4. - Colin Barker, Jan 26 2018

A255997 Number of length n+6 0..1 arrays with at most one downstep in every n consecutive neighbor pairs.

Original entry on oeis.org

128, 256, 354, 451, 568, 705, 854, 1016, 1192, 1383, 1590, 1814, 2056, 2317, 2598, 2900, 3224, 3571, 3942, 4338, 4760, 5209, 5686, 6192, 6728, 7295, 7894, 8526, 9192, 9893, 10630, 11404, 12216, 13067, 13958, 14890, 15864, 16881, 17942, 19048, 20200

Offset: 1

R. H. Hardin, Mar 13 2015

nonn

Row 6 of A255992.

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

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

Cf. A255992.

Empirical: a(n) = (1/6)*n^3 + 3*n^2 + (533/6)*n + 28 for n>4.

Empirical g.f.: x*(128 - 256*x + 98*x^2 + 59*x^3 - 8*x^4 - 21*x^5 - 8*x^6 + 9*x^7) / (1 - x)^4. - Colin Barker, Jan 26 2018

A255998 Number of length n+7 0..1 arrays with at most one downstep in every n consecutive neighbor pairs.

Original entry on oeis.org

256, 512, 667, 796, 945, 1134, 1352, 1584, 1831, 2094, 2374, 2672, 2989, 3326, 3684, 4064, 4467, 4894, 5346, 5824, 6329, 6862, 7424, 8016, 8639, 9294, 9982, 10704, 11461, 12254, 13084, 13952, 14859, 15806, 16794, 17824, 18897, 20014, 21176, 22384, 23639

Offset: 1

R. H. Hardin, Mar 13 2015

nonn

Row 7 of A255992.

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

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

Cf. A255992.

Empirical: a(n) = (1/6)*n^3 + (7/2)*n^2 + (454/3)*n + 64 for n>5.

Empirical g.f.: x*(256 - 512*x + 155*x^2 + 176*x^3 - 29*x^4 - 26*x^5 - 31*x^6 - 4*x^7 + 16*x^8) / (1 - x)^4. - Colin Barker, Jan 26 2018

cp's OEIS Frontend

A255993 Number of length n+2 0..1 arrays with at most one downstep in every n consecutive neighbor pairs.

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A255988 Number of length n+4 0..1 arrays with at most one downstep in every 4 consecutive neighbor pairs.

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A255989 Number of length n+5 0..1 arrays with at most one downstep in every 5 consecutive neighbor pairs.

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A255990 Number of length n+6 0..1 arrays with at most one downstep in every 6 consecutive neighbor pairs.

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A255991 Number of length n+7 0..1 arrays with at most one downstep in every 7 consecutive neighbor pairs.

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A255994 Number of length n+3 0..1 arrays with at most one downstep in every n consecutive neighbor pairs.

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A255995 Number of length n+4 0..1 arrays with at most one downstep in every n consecutive neighbor pairs.

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A255996 Number of length n+5 0..1 arrays with at most one downstep in every n consecutive neighbor pairs.

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A255997 Number of length n+6 0..1 arrays with at most one downstep in every n consecutive neighbor pairs.

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