A241964 -id:A241964 - cp's OEIS frontend

A241960 Number of length n+3 0..4 arrays with no consecutive four elements summing to more than 2*4.

355, 1421, 5778, 23320, 92037, 365810, 1460409, 5830838, 23237977, 92595629, 369142639, 1471836335, 5867774115, 23391443650, 93250841634, 371756884287, 1482053418845, 5908333573340, 23554074220207, 93900552089203

Offset: 1

R. H. Hardin, May 03 2014

nonn

Column 4 of A241964

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 85

Empirical recurrence of order 85 (see link above)

A241961 Number of length n+3 0..5 arrays with no consecutive four elements summing to more than 2*5.

Original entry on oeis.org

721, 3437, 16660, 80132, 376559, 1782453, 8476317, 40313706, 191370192, 908268343, 4312922647, 20483132941, 97267496309, 461856616822, 2193101268453, 10414092378458, 49451882143389, 234822848509532, 1115058584108581

Offset: 1

R. H. Hardin, May 03 2014

nonn

Column 5 of A241964.

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

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

Cf. A241964.

A241962 Number of length n+3 0..6 arrays with no consecutive four elements summing to more than 2*6.

Original entry on oeis.org

1316, 7280, 40978, 228826, 1247602, 6853011, 37822419, 208778442, 1150195313, 6335359100, 34913522464, 192436464511, 1060537739121, 5844288421834, 32206928983867, 177491988769402, 978153244754765, 5390524419041649

Offset: 1

R. H. Hardin, May 03 2014

nonn

Column 6 of A241964

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

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

A241963 Number of length n+3 0..7 arrays with no consecutive four elements summing to more than 2*7.

Original entry on oeis.org

2220, 13980, 89622, 569874, 3536286, 22111157, 138925925, 873035589, 5475318946, 34331845408, 215383294448, 1351453881412, 8478796110164, 53190349676453, 333690439881015, 2093470677473842, 13133749568417338, 82396056288048569

Offset: 1

R. H. Hardin, May 03 2014

nonn

Column 7 of A241964

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

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

A241965 Number of length 2+3 0..n arrays with no consecutive four elements summing to more than 2*n.

Original entry on oeis.org

19, 124, 486, 1421, 3437, 7280, 13980, 24897, 41767, 66748, 102466, 152061, 219233, 308288, 424184, 572577, 759867, 993244, 1280734, 1631245, 2054613, 2561648, 3164180, 3875105, 4708431, 5679324, 6804154, 8100541, 9587401, 11284992

Offset: 1

R. H. Hardin, May 03 2014

nonn

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

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

Row 2 of A241964.

Empirical: a(n) = (23/60)*n^5 + (9/4)*n^4 + (21/4)*n^3 + (25/4)*n^2 + (58/15)*n + 1.
Conjectures from Colin Barker, Oct 31 2018: (Start)
G.f.: x*(19 + 10*x + 27*x^2 - 15*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)

A241966 Number of length 3+3 0..n arrays with no consecutive four elements summing to more than 2*n.

Original entry on oeis.org

33, 311, 1597, 5778, 16660, 40978, 89622, 179079, 333091, 584529, 977483, 1569568, 2434446, 3664564, 5374108, 7702173, 10816149, 14915323, 20234697, 27049022, 35677048, 46485990, 59896210, 76386115, 96497271, 120839733, 150097591

Offset: 1

R. H. Hardin, May 03 2014

nonn

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

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

Row 3 of A241964.

Empirical: a(n) = (3/10)*n^6 + (127/60)*n^5 + (149/24)*n^4 + (59/6)*n^3 + (1079/120)*n^2 + (91/20)*n + 1.
Conjectures from Colin Barker, Oct 31 2018: (Start)
G.f.: x*(33 + 80*x + 113*x^2 - 25*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)

A241967 Number of length 4+3 0..n arrays with no consecutive four elements summing to more than 2*n.

Original entry on oeis.org

57, 775, 5211, 23320, 80132, 228826, 569874, 1277427, 2634115, 5075433, 9244885, 16061058, 26797798, 43178660, 67486804, 102691509, 152592477, 221983099, 316833855, 444497020, 613933848, 835965406, 1123548230, 1492075975

Offset: 1

R. H. Hardin, May 03 2014

nonn

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

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

Row 4 of A241964.

Empirical: a(n) = (293/1260)*n^7 + (691/360)*n^6 + (2443/360)*n^5 + (121/9)*n^4 + (5857/360)*n^3 + (4369/360)*n^2 + (2189/420)*n + 1.
Conjectures from Colin Barker, Oct 31 2018: (Start)
G.f.: x*(57 + 319*x + 607*x^2 + 140*x^3 + 70*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)

A241968 Number of length 5+3 0..n arrays with no consecutive four elements summing to more than 2*n.

Original entry on oeis.org

97, 1895, 16649, 92037, 376559, 1247602, 3536286, 8889273, 20314789, 42967177, 85231367, 160175717, 287448747, 495702356, 825631180, 1333724817, 2096836713, 3217680571, 4831372213, 7113141893, 10287349127, 14637939174, 20520487370

Offset: 1

R. H. Hardin, May 03 2014

nonn

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

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

Row 5 of A241964.

Empirical: a(n) = (589/3360)*n^8 + (349/210)*n^7 + (2483/360)*n^6 + (1317/80)*n^5 + (35819/1440)*n^4 + (1963/80)*n^3 + (19597/1260)*n^2 + (613/105)*n + 1.
Conjectures from Colin Barker, Oct 31 2018: (Start)
G.f.: x*(97 + 1022*x + 3086*x^2 + 2268*x^3 + 632*x^4 - 65*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)

A241969 Number of length 6+3 0..n arrays with no consecutive four elements summing to more than 2*n.

Original entry on oeis.org

166, 4663, 53553, 365810, 1782453, 6853011, 22111157, 62336336, 157897575, 366623400, 792037896, 1610247431, 3108255424, 5737023770, 10183189142, 17463980371, 29050569460, 47025823517, 74283207995, 114774423104

Offset: 1

R. H. Hardin, May 03 2014

nonn

Row 6 of A241964

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

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

Empirical: a(n) = (24187/181440)*n^9 + (57493/40320)*n^8 + (12829/1890)*n^7 + (54583/2880)*n^6 + (296887/8640)*n^5 + (242891/5760)*n^4 + (3196213/90720)*n^3 + (196087/10080)*n^2 + (16343/2520)*n + 1

A241970 Number of length 7+3 0..n arrays with no consecutive four elements summing to more than 2*n.

Original entry on oeis.org

285, 11518, 172980, 1460409, 8476317, 37822419, 138925925, 439298830, 1233421948, 3144133223, 7397932763, 16271365032, 33784971650, 66744596242, 126257435694, 229882539967, 404612835239, 690928552540, 1148210556166

Offset: 1

R. H. Hardin, May 03 2014

nonn

Row 7 of A241964

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

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

Empirical: a(n) = (1057/10368)*n^10 + (16313/13440)*n^9 + (787993/120960)*n^8 + (139919/6720)*n^7 + (760961/17280)*n^6 + (124127/1920)*n^5 + (3473863/51840)*n^4 + (20441/420)*n^3 + (240259/10080)*n^2 + (2001/280)*n + 1

cp's OEIS Frontend

A241960 Number of length n+3 0..4 arrays with no consecutive four elements summing to more than 2*4.

Views

Author

Keywords

Comments

Examples

Links

Formula

A241961 Number of length n+3 0..5 arrays with no consecutive four elements summing to more than 2*5.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A241962 Number of length n+3 0..6 arrays with no consecutive four elements summing to more than 2*6.

Views

Author

Keywords

Comments

Examples

Links

A241963 Number of length n+3 0..7 arrays with no consecutive four elements summing to more than 2*7.

Views

Author

Keywords

Comments

Examples

Links

A241965 Number of length 2+3 0..n arrays with no consecutive four elements summing to more than 2*n.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A241966 Number of length 3+3 0..n arrays with no consecutive four elements summing to more than 2*n.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A241967 Number of length 4+3 0..n arrays with no consecutive four elements summing to more than 2*n.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A241968 Number of length 5+3 0..n arrays with no consecutive four elements summing to more than 2*n.

Views

Author

Keywords

Examples

Links

Crossrefs

Formula

A241969 Number of length 6+3 0..n arrays with no consecutive four elements summing to more than 2*n.

Views

Author

Keywords

Comments

Examples

Links

Formula

A241970 Number of length 7+3 0..n arrays with no consecutive four elements summing to more than 2*n.

Views

Author

Keywords

Comments

Examples

Links

Formula