A242144 -id:A242144 - cp's OEIS frontend

A242140 Number of length n+5 0..4 arrays with no consecutive six elements summing to more than 3*4.

8688, 36224, 154647, 663395, 2837837, 12043599, 50455611, 212162746, 895579480, 3787247400, 16020690930, 67729965951, 286080148023, 1208022059263, 5102043513434, 21553426093066, 91062071731465, 384728908620213

Offset: 1

R. H. Hardin, May 05 2014

nonn

Column 4 of A242144

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

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

A242141 Number of length n+5 0..5 arrays with no consecutive six elements summing to more than 3*5.

Original entry on oeis.org

25494, 126894, 647404, 3319500, 16970962, 86052208, 430518585, 2162172742, 10902502273, 55078322417, 278343334238, 1405766614019, 7093088366242, 35779370687575, 180515721830508, 910971025811519, 4597754179265792

Offset: 1

R. H. Hardin, May 05 2014

nonn

Column 5 of A242144

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

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

A242142 Number of length n+5 0..6 arrays with no consecutive six elements summing to more than 3*6.

Original entry on oeis.org

63490, 367358, 2180310, 13006484, 77357343, 456215409, 2653766000, 15497830900, 90878735732, 533945267676, 3138209023516, 18432820158203, 108162937167014, 634507293368503, 3722906161866317, 21849327869647678, 128247123968241090

Offset: 1

R. H. Hardin, May 05 2014

nonn

Column 6 of A242144

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

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

A242143 Number of length n+5 0..7 arrays with no consecutive six elements summing to more than 3*7.

Original entry on oeis.org

140148, 924300, 6256170, 42564898, 288712815, 1941492045, 12874102578, 85713766385, 573062988542, 3838977344664, 25726636932711, 172293701892093, 1152716573289716, 7709820824430357, 51576900836608142, 345127323266038809

Offset: 1

R. H. Hardin, May 05 2014

nonn

Column 7 of A242144

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

R. H. Hardin, Table of n, a(n) for n = 1..155

A242145 Number of length 1+5 0..n arrays with no consecutive six elements summing to more than 3*n.

Original entry on oeis.org

42, 435, 2338, 8688, 25494, 63490, 140148, 282051, 527626, 930237, 1561638, 2515786, 3913014, 5904564, 8677480, 12459861, 17526474, 24204727, 32881002, 44007348, 58108534, 75789462, 97742940, 124757815, 157727466, 197658657

Offset: 1

R. H. Hardin, May 05 2014

nonn

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

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

Row 1 of A242144.

Empirical: a(n) = (1/2)*n^6 + (131/40)*n^5 + (71/8)*n^4 + (103/8)*n^3 + (85/8)*n^2 + (97/20)*n + 1.
Conjectures from Colin Barker, Oct 31 2018: (Start)
G.f.: x*(42 + 141*x + 175*x^2 - 13*x^3 + 21*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)

A242146 Number of length 2+5 0..n arrays with no consecutive six elements summing to more than 3*n.

Original entry on oeis.org

74, 1113, 7862, 36224, 126894, 367358, 924300, 2088459, 4333978, 8394287, 15356562, 26776802, 44817566, 72410412, 113445080, 172987461, 257528394, 375265333, 536418926, 753586548, 1042134830, 1420633226, 1911330660

Offset: 1

R. H. Hardin, May 05 2014

nonn

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

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

Row 2 of A242144.

Empirical: a(n) = (1021/2520)*n^7 + (28/9)*n^6 + (3679/360)*n^5 + (1349/72)*n^4 + (1873/90)*n^3 + (1019/72)*n^2 + (779/140)*n + 1.
Conjectures from Colin Barker, Oct 31 2018: (Start)
G.f.: x*(74 + 521*x + 1030*x^2 + 348*x^3 + 90*x^4 - 28*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)

A242147 Number of length 3+5 0..n arrays with no consecutive six elements summing to more than 3*n.

Original entry on oeis.org

132, 2902, 27024, 154647, 647404, 2180310, 6256170, 15876783, 36560854, 77812152, 155155078, 292868433, 527561802, 912752596, 1524615420, 2469089061, 3890540016, 5982195106, 8998569348, 13270128883, 19220442384, 27386087994

Offset: 1

R. H. Hardin, May 05 2014

nonn

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

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

Row 3 of A242144.

Empirical: a(n) = (757/2240)*n^8 + (14969/5040)*n^7 + (16439/1440)*n^6 + (1133/45)*n^5 + (100771/2880)*n^4 + (22733/720)*n^3 + (92011/5040)*n^2 + (879/140)*n + 1.
Conjectures from Colin Barker, Oct 31 2018: (Start)
G.f.: x*(132 + 1714*x + 5658*x^2 + 4815*x^3 + 1309*x^4 - 30*x^5 + 36*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)

A242148 Number of length 4+5 0..n arrays with no consecutive six elements summing to more than 3*n.

Original entry on oeis.org

236, 7596, 93308, 663395, 3319500, 13006484, 42564898, 121330981, 310054250, 725133024, 1576001362, 3220436895, 6243597894, 11567739640, 20600804748, 35433429545, 59095358912, 95883815172, 151778022640, 234955848347

Offset: 1

R. H. Hardin, May 05 2014

nonn

Row 4 of A242144

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

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

Empirical: a(n) = (51431/181440)*n^9 + (7069/2520)*n^8 + (373229/30240)*n^7 + (763/24)*n^6 + (457907/8640)*n^5 + (1191/20)*n^4 + (2059039/45360)*n^3 + (5759/252)*n^2 + (4399/630)*n + 1

A242149 Number of length 5+5 0..n arrays with no consecutive six elements summing to more than 3*n.

Original entry on oeis.org

421, 19834, 321320, 2837837, 16970962, 77357343, 288712815, 924335053, 2621131557, 6736000381, 15956886023, 35297721979, 73650614324, 146121877010, 277441759058, 506811766161, 894639234101, 1531707118508, 2551438684546

Offset: 1

R. H. Hardin, May 05 2014

nonn

Row 5 of A242144

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

R. H. Hardin, Table of n, a(n) for n = 1..137

Empirical: a(n) = (859693/3628800)*n^10 + (1892767/725760)*n^9 + (1563833/120960)*n^8 + (4608661/120960)*n^7 + (12804769/172800)*n^6 + (3445219/34560)*n^5 + (1069993/11340)*n^4 + (11327921/181440)*n^3 + (234169/8400)*n^2 + (2416/315)*n + 1

A242150 Number of length 6+5 0..n arrays with no consecutive six elements summing to more than 3*n.

Original entry on oeis.org

747, 51440, 1098260, 12043599, 86052208, 456215409, 1941492045, 6980495147, 21963123129, 62016006945, 160112849845, 383388390463, 860906165796, 1828944557550, 3702209669222, 7182352124565, 13418860449679, 24241936676342

Offset: 1

R. H. Hardin, May 05 2014

nonn

Row 6 of A242144

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

R. H. Hardin, Table of n, a(n) for n = 1..48

Empirical: a(n) = (1956631/9979200)*n^11 + (1726129/725760)*n^10 + (9526243/725760)*n^9 + (5272471/120960)*n^8 + (19548049/201600)*n^7 + (5255677/34560)*n^6 + (124917323/725760)*n^5 + (25617881/181440)*n^4 + (75074821/907200)*n^3 + (83833/2520)*n^2 + (115589/13860)*n + 1

cp's OEIS Frontend

A242140 Number of length n+5 0..4 arrays with no consecutive six elements summing to more than 3*4.

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A242141 Number of length n+5 0..5 arrays with no consecutive six elements summing to more than 3*5.

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A242142 Number of length n+5 0..6 arrays with no consecutive six elements summing to more than 3*6.

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A242143 Number of length n+5 0..7 arrays with no consecutive six elements summing to more than 3*7.

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A242145 Number of length 1+5 0..n arrays with no consecutive six elements summing to more than 3*n.

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A242146 Number of length 2+5 0..n arrays with no consecutive six elements summing to more than 3*n.

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A242147 Number of length 3+5 0..n arrays with no consecutive six elements summing to more than 3*n.

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A242148 Number of length 4+5 0..n arrays with no consecutive six elements summing to more than 3*n.

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A242149 Number of length 5+5 0..n arrays with no consecutive six elements summing to more than 3*n.

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A242150 Number of length 6+5 0..n arrays with no consecutive six elements summing to more than 3*n.

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