A249001 -id:A249001 - cp's OEIS frontend

A248995 Number of length n+4 0..2 arrays with no five consecutive terms having two times the sum of any three elements equal to three times the sum of the remaining two.

190, 464, 1140, 2802, 6872, 16800, 41084, 100590, 246378, 603406, 1477382, 3616932, 8855718, 21683810, 53094696, 130003772, 318312974, 779389186, 1908348180, 4672636566, 11441043846, 28013571820, 68591653930, 167947819478

Offset: 1

R. H. Hardin, Oct 18 2014

nonn

Column 2 of A249001

			Some solutions for n=6
..0....0....1....1....1....0....2....2....0....0....2....2....2....0....0....0
..0....1....1....0....2....1....1....0....1....2....0....0....1....1....1....1
..2....2....1....2....1....2....1....2....2....0....2....0....0....1....2....0
..0....1....2....1....2....1....0....1....0....2....2....0....2....2....0....2
..0....2....2....0....0....2....2....2....0....0....0....1....2....2....0....1
..0....0....2....0....2....1....2....2....0....2....2....1....1....0....0....2
..1....1....2....0....2....2....1....2....0....0....2....2....1....2....0....1
..0....0....0....2....2....1....2....1....2....0....0....2....1....2....1....1
..1....1....0....2....2....0....1....2....0....0....2....2....1....0....2....2
..1....0....0....0....1....2....1....2....0....1....2....2....2....0....1....0

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

Empirical: a(n) = a(n-1) +2*a(n-2) +2*a(n-3) +2*a(n-4) +16*a(n-5) -3*a(n-6) -27*a(n-7) -36*a(n-8) -41*a(n-9) -73*a(n-10) -56*a(n-11) +40*a(n-12) +103*a(n-13) +182*a(n-14) +48*a(n-15) +102*a(n-16) +147*a(n-17) +128*a(n-18) -82*a(n-19) +74*a(n-20) +90*a(n-21) -137*a(n-22) -220*a(n-23) -204*a(n-24) -4*a(n-25) -152*a(n-26) -201*a(n-27) -183*a(n-28) +54*a(n-29) -37*a(n-30) -48*a(n-31) +a(n-32) -31*a(n-33) -10*a(n-34) -8*a(n-35) +24*a(n-36) +16*a(n-37)

A248996 Number of length n+4 0..3 arrays with no five consecutive terms having two times the sum of any three elements equal to three times the sum of the remaining two.

Original entry on oeis.org

820, 2668, 8680, 28240, 91888, 299044, 973204, 3167500, 10309372, 33554728, 109215076, 355477276, 1157029012, 3765974644, 12257760052, 39897482020, 129861371368, 422682950584, 1375781835724, 4478003930896, 14575364597464

Offset: 1

R. H. Hardin, Oct 18 2014

nonn

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

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

Column 3 of A249001.

Empirical: a(n) = 3*a(n-1) + 2*a(n-2) - a(n-3) - 9*a(n-4) + 16*a(n-5) - 48*a(n-6) - 21*a(n-7) + 8*a(n-8) + 3*a(n-9).

Empirical g.f.: 4*x*(205 + 52*x - 241*x^2 - 579*x^3 - 36*x^4 - 3382*x^5 - 1168*x^6 + 563*x^7 + 192*x^8) / (1 - 3*x - 2*x^2 + x^3 + 9*x^4 - 16*x^5 + 48*x^6 + 21*x^7 - 8*x^8 - 3*x^9). - Colin Barker, Nov 09 2018

A248997 Number of length n+4 0..4 arrays with no five consecutive terms having two times the sum of any three elements equal to three times the sum of the remaining two.

Original entry on oeis.org

2540, 10360, 42308, 172888, 706704, 2888944, 11810564, 48286456, 197422012, 807188768, 3300330556, 13494048552, 55173290154, 225588339824, 922369809354, 3771323457556, 15419939994758, 63048058448056, 257786893864722

Offset: 1

R. H. Hardin, Oct 18 2014

nonn

Column 4 of A249001

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

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

A248998 Number of length n+4 0..5 arrays with no five consecutive terms having two times the sum of any three elements equal to three times the sum of the remaining two.

Original entry on oeis.org

6450, 32398, 163112, 822348, 4149708, 20952218, 105819690, 534502810, 2700047696, 13640156760, 68910290082, 348142872600, 1758874033678, 8886170481316, 44894831402844, 226818881138008, 1145942126329774

Offset: 1

R. H. Hardin, Oct 18 2014

nonn

Column 5 of A249001

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

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

A248999 Number of length n+4 0..6 arrays with no five consecutive terms having two times the sum of any three elements equal to three times the sum of the remaining two.

Original entry on oeis.org

13990, 82348, 485580, 2865126, 16909524, 99817384, 589354152, 3479916010, 20548067494, 121333048614, 716461085260, 4230692840640, 24982283288368, 147520857046232, 871114227605828, 5143954672207112, 30375223032465730

Offset: 1

R. H. Hardin, Oct 18 2014

nonn

Column 6 of A249001

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

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

A249000 Number of length n+4 0..7 arrays with no five consecutive terms having two times the sum of any three elements equal to three times the sum of the remaining two.

Original entry on oeis.org

27740, 189660, 1298968, 8902860, 61034658, 418454994, 2869206494, 19673497892, 134897701458, 924972633722, 6342399495490, 43489021952576, 298198855766202, 2044713089447888, 14020347915273238, 96135813057541116, 659191600029773658

Offset: 1

R. H. Hardin, Oct 18 2014

nonn

Column 7 of A249001

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

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

A249002 Number of length 1+4 0..n arrays with no five consecutive terms having two times the sum of any three elements equal to three times the sum of the remaining two.

Original entry on oeis.org

30, 190, 820, 2540, 6450, 13990, 27740, 50260, 86030, 139450, 217320, 325940, 475630, 674650, 937020, 1274160, 1703970, 2240850, 2908260, 3723400, 4715230, 5905430, 7328400, 9009880, 10991870, 13303750, 15994820, 19100260, 22676370

Offset: 1

R. H. Hardin, Oct 18 2014

nonn

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

R. H. Hardin, Table of n, a(n) for n = 1..209

Row 1 of A249001.

Empirical: a(n) = a(n-1) + 3*a(n-2) - a(n-3) - 5*a(n-4) - 3*a(n-5) + 6*a(n-6) + 6*a(n-7) - 3*a(n-8) - 5*a(n-9) - a(n-10) + 3*a(n-11) + a(n-12) - a(n-13).
Empirical for n mod 6 = 0: a(n) = n^5 + (185/72)*n^4 + (130/9)*n^3 - (55/6)*n^2 + (47/3)*n
Empirical for n mod 6 = 1: a(n) = n^5 + (185/72)*n^4 + (130/9)*n^3 - (65/12)*n^2 + (86/9)*n + (565/72)
Empirical for n mod 6 = 2: a(n) = n^5 + (185/72)*n^4 + (130/9)*n^3 - (55/6)*n^2 + (181/9)*n - (20/9)
Empirical for n mod 6 = 3: a(n) = n^5 + (185/72)*n^4 + (130/9)*n^3 - (65/12)*n^2 + (2/3)*n + (205/8)
Empirical for n mod 6 = 4: a(n) = n^5 + (185/72)*n^4 + (130/9)*n^3 - (55/6)*n^2 + (221/9)*n - (160/9)
Empirical for n mod 6 = 5: a(n) = n^5 + (185/72)*n^4 + (130/9)*n^3 - (65/12)*n^2 + (46/9)*n + (1685/72).
Empirical g.f.: 10*x*(3 + 16*x + 54*x^2 + 118*x^3 + 179*x^4 + 178*x^5 + 143*x^6 + 84*x^7 + 44*x^8 + 24*x^9 + 21*x^10) / ((1 - x)^6*(1 + x)^3*(1 + x + x^2)^2). - Colin Barker, Nov 09 2018

A249003 Number of length 2+4 0..n arrays with no five consecutive terms having two times the sum of any three elements equal to three times the sum of the remaining two.

Original entry on oeis.org

58, 464, 2668, 10360, 32398, 82348, 189660, 387900, 744378, 1335780, 2289960, 3737824, 5914730, 9025016, 13447116, 19506256, 27749742, 38646260, 53006324, 71470164, 95143346, 124907012, 162219976, 208226592, 264893594, 333635648

Offset: 1

R. H. Hardin, Oct 18 2014

nonn

Row 2 of A249001

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

R. H. Hardin, Table of n, a(n) for n = 1..95

A249004 Number of length 3+4 0..n arrays with no five consecutive terms having two times the sum of any three elements equal to three times the sum of the remaining two.

Original entry on oeis.org

112, 1140, 8680, 42308, 163112, 485580, 1298968, 2997774, 6449496, 12811158, 24159584, 42911184, 73629888, 120844328, 193152322, 298869080, 452268778, 666984964, 966771826, 1372738118, 1920965096, 2643444158, 3592832436

Offset: 1

R. H. Hardin, Oct 18 2014

nonn

Row 3 of A249001

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

R. H. Hardin, Table of n, a(n) for n = 1..69

A249005 Number of length 4+4 0..n arrays with no five consecutive terms having two times the sum of any three elements equal to three times the sum of the remaining two.

Original entry on oeis.org

216, 2802, 28240, 172888, 822348, 2865126, 8902860, 23177368, 55906496, 122921570, 254998668, 492803174, 916912140, 1618570176, 2775224082, 4580364152, 7372967710, 11513855042, 17636594106, 26371506592, 38792087628

Offset: 1

R. H. Hardin, Oct 18 2014

nonn

Row 4 of A249001

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

R. H. Hardin, Table of n, a(n) for n = 1..69

cp's OEIS Frontend

A248995 Number of length n+4 0..2 arrays with no five consecutive terms having two times the sum of any three elements equal to three times the sum of the remaining two.

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A248996 Number of length n+4 0..3 arrays with no five consecutive terms having two times the sum of any three elements equal to three times the sum of the remaining two.

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A248997 Number of length n+4 0..4 arrays with no five consecutive terms having two times the sum of any three elements equal to three times the sum of the remaining two.

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A248998 Number of length n+4 0..5 arrays with no five consecutive terms having two times the sum of any three elements equal to three times the sum of the remaining two.

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A248999 Number of length n+4 0..6 arrays with no five consecutive terms having two times the sum of any three elements equal to three times the sum of the remaining two.

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A249000 Number of length n+4 0..7 arrays with no five consecutive terms having two times the sum of any three elements equal to three times the sum of the remaining two.

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A249002 Number of length 1+4 0..n arrays with no five consecutive terms having two times the sum of any three elements equal to three times the sum of the remaining two.

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A249003 Number of length 2+4 0..n arrays with no five consecutive terms having two times the sum of any three elements equal to three times the sum of the remaining two.

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A249004 Number of length 3+4 0..n arrays with no five consecutive terms having two times the sum of any three elements equal to three times the sum of the remaining two.

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A249005 Number of length 4+4 0..n arrays with no five consecutive terms having two times the sum of any three elements equal to three times the sum of the remaining two.

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