A200838 -id:A200838 - cp's OEIS frontend

A200833 Number of 0..3 arrays x(0..n+1) of n+2 elements without any two consecutive increases or two consecutive decreases.

56, 194, 676, 2356, 8210, 28610, 99700, 347434, 1210736, 4219166, 14702926, 51236674, 178549274, 622207508, 2168265232, 7555958512, 26330961818, 91757987972, 319757721532, 1114289913490, 3883071237050, 13531704854780

Offset: 1

R. H. Hardin Nov 23 2011

nonn

Column 3 of A200838.

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

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

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

Empirical g.f.: 2*x*(28 - 15*x + 6*x^2 - 8*x^3) / (1 - 4*x + 2*x^2 - x^3 + x^4). - Colin Barker, Oct 14 2017

A200834 Number of 0..4 arrays x(0..n+1) of n+2 elements without any two consecutive increases or two consecutive decreases.

Original entry on oeis.org

105, 435, 1817, 7587, 31677, 132263, 552247, 2305835, 9627715, 40199277, 167846875, 700822891, 2926195229, 12217949255, 51014464969, 213004292437, 889371840403, 3713456951747, 15505058633553, 64739364520389

Offset: 1

R. H. Hardin Nov 23 2011

nonn

Column 4 of A200838.

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

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

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

Empirical g.f.: x*(105 - 90*x + 62*x^2 - 73*x^3 + 20*x^4 - 25*x^5) / ((1 - x)*(1 - 4*x - 3*x^3 - x^5)). - Colin Barker, Oct 14 2017

A200835 Number of 0..5 arrays x(0..n+1) of n+2 elements without any two consecutive increases or two consecutive decreases.

Original entry on oeis.org

176, 846, 4108, 19930, 96690, 469116, 2276028, 11042700, 53576350, 259938722, 1261156090, 6118806300, 29686880836, 144033141554, 698811908924, 3390456382404, 16449625906804, 79809371351400, 387214626739458

Offset: 1

R. H. Hardin Nov 23 2011

nonn

Column 5 of A200838.

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

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

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

Empirical g.f.: 2*x*(88 - 105*x + 44*x^2 - 85*x^3 + 50*x^4 - 33*x^5 + 18*x^6) / (1 - 6*x + 6*x^2 - 3*x^3 + 5*x^4 - 3*x^5 + 2*x^6 - x^7). - Colin Barker, Oct 14 2017

A200836 Number of 0..6 arrays x(0..n+1) of n+2 elements without any two consecutive increases or two consecutive decreases.

Original entry on oeis.org

273, 1491, 8239, 45465, 250913, 1384813, 7642875, 42181611, 232803603, 1284861277, 7091249941, 39137163521, 216001069269, 1192126810953, 6579441195743, 36312451033865, 200411259993515, 1106085433196691

Offset: 1

R. H. Hardin, Nov 23 2011

nonn

Column 6 of A200838.

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

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

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

Empirical g.f.: x*(273 - 420*x + 259*x^2 - 427*x^3 + 320*x^4 - 319*x^5 + 236*x^6 - 91*x^7 + 49*x^8) / (1 - 7*x + 9*x^2 - 6*x^3 + 9*x^4 - 7*x^5 + 7*x^6 - 5*x^7 + 2*x^8 - x^9). - Colin Barker, Oct 15 2017

A200837 Number of 0..7 arrays x(0..n+1) of n+2 elements without any two consecutive increases or two consecutive decreases.

Original entry on oeis.org

400, 2444, 15128, 93472, 577660, 3570086, 22063924, 136360286, 842739040, 5208328180, 32188710564, 198933910242, 1229459024390, 7598350081290, 46959616234372, 290221631449614, 1793638920327662, 11085116434803236

Offset: 1

R. H. Hardin, Nov 23 2011

nonn

Column 7 of A200838.

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

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

Empirical: a(n) = 8*a(n-1) -12*a(n-2) +6*a(n-3) -10*a(n-4) +12*a(n-5) -11*a(n-6) +11*a(n-7) -6*a(n-8) +3*a(n-9) -a(n-10).

Empirical g.f.: 2*x*(200 - 378*x + 188*x^2 - 312*x^3 + 378*x^4 - 329*x^5 + 338*x^6 - 183*x^7 + 92*x^8 - 32*x^9) / (1 - 8*x + 12*x^2 - 6*x^3 + 10*x^4 - 12*x^5 + 11*x^6 - 11*x^7 + 6*x^8 - 3*x^9 + x^10). - Colin Barker, Oct 16 2017

A200839 Number of 0..n arrays x(0..3) of 4 elements without any two consecutive increases or two consecutive decreases.

Original entry on oeis.org

16, 69, 194, 435, 846, 1491, 2444, 3789, 5620, 8041, 11166, 15119, 20034, 26055, 33336, 42041, 52344, 64429, 78490, 94731, 113366, 134619, 158724, 185925, 216476, 250641, 288694, 330919, 377610, 429071, 485616, 547569, 615264, 689045, 769266

Offset: 1

R. H. Hardin Nov 23 2011

nonn

Row 2 of A200838.

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

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

Empirical: a(n) = (5/12)*n^4 + (19/6)*n^3 + (79/12)*n^2 + (29/6)*n + 1.
Conjectures from Colin Barker, Oct 14 2017: (Start)
G.f.: x*(16 - 11*x + 9*x^2 - 5*x^3 + x^4) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
(End)

A200840 Number of 0..n arrays x(0..4) of 5 elements without any two consecutive increases or two consecutive decreases.

Original entry on oeis.org

32, 191, 676, 1817, 4108, 8239, 15128, 25953, 42184, 65615, 98396, 143065, 202580, 280351, 380272, 506753, 664752, 859807, 1098068, 1386329, 1732060, 2143439, 2629384, 3199585, 3864536, 4635567, 5524876, 6545561, 7711652, 9038143

Offset: 1

R. H. Hardin Nov 23 2011

nonn

Row 3 of A200838.

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

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

Empirical: a(n) = (4/15)*n^5 + (17/6)*n^4 + (28/3)*n^3 + (73/6)*n^2 + (32/5)*n + 1.
Conjectures from Colin Barker, Oct 14 2017: (Start)
G.f.: x*(32 - x + 10*x^2 - 14*x^3 + 6*x^4 - x^5) / (1 - x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
(End)

A200841 Number of 0..n arrays x(0..5) of 6 elements without any two consecutive increases or two consecutive decreases.

Original entry on oeis.org

64, 529, 2356, 7587, 19930, 45465, 93472, 177381, 315844, 533929, 864436, 1349335, 2041326, 3005521, 4321248, 6083977, 8407368, 11425441, 15294868, 20197387, 26342338, 33969321, 43350976, 54795885, 68651596, 85307769, 105199444

Offset: 1

R. H. Hardin Nov 23 2011

nonn

Row 4 of A200838.

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

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

Empirical: a(n) = (61/360)*n^6 + (93/40)*n^5 + (779/72)*n^4 + (521/24)*n^3 + (1801/90)*n^2 + (239/30)*n + 1.
Conjectures from Colin Barker, Oct 14 2017: (Start)
G.f.: x*(64 + 81*x - 3*x^2 - 36*x^3 + 22*x^4 - 7*x^5 + x^6) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)

A200842 Number of 0..n arrays x(0..6) of 7 elements without any two consecutive increases or two consecutive decreases.

Original entry on oeis.org

128, 1465, 8210, 31677, 96690, 250913, 577660, 1212729, 2365804, 4346969, 7598878, 12735125, 20585358, 32247681, 49148888, 73113073, 106439160, 151987897, 213278858, 294597997, 401116298, 539020065, 715653396, 939673385, 1221218596

Offset: 1

R. H. Hardin Nov 23 2011

nonn

Row 5 of A200838.

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

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

Empirical: a(n) = (34/315)*n^7 + (163/90)*n^6 + (1981/180)*n^5 + (557/18)*n^4 + (7807/180)*n^3 + (1361/45)*n^2 + (333/35)*n + 1.
Conjectures from Colin Barker, Oct 14 2017: (Start)
G.f.: x*(128 + 441*x + 74*x^2 - 151*x^3 + 74*x^4 - 29*x^5 + 8*x^6 - x^7) / (1 - x)^8.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
(End)

A200843 Number of 0..n arrays x(0..7) of 8 elements without any two consecutive increases or two consecutive decreases.

Original entry on oeis.org

256, 4057, 28610, 132263, 469116, 1384813, 3570086, 8291391, 17720746, 35389651, 66794740, 120185585, 207567842, 345957699, 558926356, 878476037, 1347291804, 2021416213, 2973396622, 4295957731, 6106254704, 8550764993, 11810879754

Offset: 1

R. H. Hardin Nov 23 2011

nonn

Row 6 of A200838.

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

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

Empirical: a(n) = (277/4032)*n^8 + (1375/1008)*n^7 + (4933/480)*n^6 + (2723/72)*n^5 + (14161/192)*n^4 + (11197/144)*n^3 + (216211/5040)*n^2 + (929/84)*n + 1.
Conjectures from Colin Barker, Oct 14 2017: (Start)
G.f.: x*(256 + 1753*x + 1313*x^2 - 679*x^3 + 177*x^4 - 77*x^5 + 35*x^6 - 9*x^7 + x^8) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.
(End)

cp's OEIS Frontend

A200833 Number of 0..3 arrays x(0..n+1) of n+2 elements without any two consecutive increases or two consecutive decreases.

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A200834 Number of 0..4 arrays x(0..n+1) of n+2 elements without any two consecutive increases or two consecutive decreases.

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A200835 Number of 0..5 arrays x(0..n+1) of n+2 elements without any two consecutive increases or two consecutive decreases.

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A200836 Number of 0..6 arrays x(0..n+1) of n+2 elements without any two consecutive increases or two consecutive decreases.

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A200837 Number of 0..7 arrays x(0..n+1) of n+2 elements without any two consecutive increases or two consecutive decreases.

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A200839 Number of 0..n arrays x(0..3) of 4 elements without any two consecutive increases or two consecutive decreases.

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A200840 Number of 0..n arrays x(0..4) of 5 elements without any two consecutive increases or two consecutive decreases.

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A200841 Number of 0..n arrays x(0..5) of 6 elements without any two consecutive increases or two consecutive decreases.

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A200842 Number of 0..n arrays x(0..6) of 7 elements without any two consecutive increases or two consecutive decreases.

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A200843 Number of 0..n arrays x(0..7) of 8 elements without any two consecutive increases or two consecutive decreases.

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