A249290 -id:A249290 - cp's OEIS frontend

A249284 Number of length n+3 0..2 arrays with no four consecutive terms having the sum of any three elements equal to three times the fourth.

66, 168, 428, 1094, 2792, 7132, 18232, 46616, 119176, 304696, 779066, 1992002, 5093330, 13023126, 33299000, 85142802, 217703012, 556648464, 1423304428, 3639273226, 9305324178, 23792953554, 60836640416, 155554327024, 397739724496

Offset: 1

R. H. Hardin, Oct 24 2014

nonn

Column 2 of A249290

			Some solutions for n=9
..1....0....2....2....1....1....0....1....1....1....0....1....1....2....2....1
..1....0....1....0....0....1....1....0....1....0....0....1....1....0....1....0
..0....1....0....0....2....0....2....2....2....2....0....1....2....0....0....2
..1....0....0....0....2....1....0....2....2....0....2....2....1....0....0....2
..0....1....2....1....0....0....0....0....1....2....2....2....2....1....1....2
..2....0....2....0....0....0....0....1....2....1....0....0....2....0....1....0
..0....1....2....0....0....1....2....0....2....2....2....2....1....0....0....0
..2....1....0....1....1....1....0....1....2....1....0....2....0....1....0....2
..0....0....0....1....2....0....2....0....0....2....2....1....0....0....2....2
..2....0....2....1....2....1....1....0....0....1....1....2....0....2....1....2
..2....0....2....2....1....0....2....0....1....2....2....0....2....0....2....1
..2....2....1....2....2....0....2....1....2....0....1....0....2....0....2....0

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

Empirical: a(n) = a(n-1) +2*a(n-2) +3*a(n-3) +7*a(n-4) +a(n-5) -6*a(n-6) -12*a(n-7) -14*a(n-8) -14*a(n-9) -7*a(n-10) +3*a(n-11) +2*a(n-12)

A249285 Number of length n+3 0..3 arrays with no four consecutive terms having the sum of any three elements equal to three times the fourth.

Original entry on oeis.org

204, 660, 2144, 6960, 22572, 73204, 237480, 770416, 2499164, 8107012, 26298608, 85311248, 276744204, 897739412, 2912207432, 9447011744, 30645489228, 99411957620, 322485877472, 1046123080816, 3393554802188, 11008469603188

Offset: 1

R. H. Hardin, Oct 24 2014

nonn

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

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

Column 3 of A249290.

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

Empirical g.f.: 4*x*(51 + 63*x + 104*x^2 + 134*x^3 + 23*x^4 - 133*x^5 - 18*x^6 + 48*x^7) / (1 - 2*x - 2*x^2 - 4*x^3 - 8*x^4 - 4*x^5 + 8*x^6 + 2*x^7 - 3*x^8). - Colin Barker, Nov 09 2018

A249286 Number of length n+3 0..4 arrays with no four consecutive terms having the sum of any three elements equal to three times the fourth.

Original entry on oeis.org

524, 2228, 9504, 40588, 173368, 740616, 3164312, 13520668, 57772560, 246857788, 1054810472, 4507167504, 19258980852, 82293014888, 351635522044, 1502528043892, 6420257600360, 27433569837528, 117222829267252

Offset: 1

R. H. Hardin, Oct 24 2014

nonn

Column 4 of A249290.

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

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

Cf. A249290.

Empirical: a(n) = 3*a(n-1) +3*a(n-2) +9*a(n-3) +35*a(n-4) -65*a(n-5) -151*a(n-6) -317*a(n-7) -534*a(n-8) -140*a(n-9) +1280*a(n-10) +2126*a(n-11) +2048*a(n-12) +5830*a(n-13) +4946*a(n-14) +11778*a(n-15) +25333*a(n-16) +19483*a(n-17) -11542*a(n-18) -9074*a(n-19) -7639*a(n-20) -13027*a(n-21) +38961*a(n-22) -25267*a(n-23) -187805*a(n-24) -120777*a(n-25) +143132*a(n-26) +88370*a(n-27) -57497*a(n-28) -100517*a(n-29) -152210*a(n-30) -3304*a(n-31) +156512*a(n-32) +254068*a(n-33) +111836*a(n-34) -84272*a(n-35) -31976*a(n-36) +9504*a(n-37) -3632*a(n-38) -144*a(n-39) +576*a(n-40).

A249287 Number of length n+3 0..5 arrays with no four consecutive terms having the sum of any three elements equal to three times the fourth.

Original entry on oeis.org

1098, 5646, 29100, 150112, 774542, 3996816, 20626236, 106449362, 549377682, 2835311880, 14632955578, 75520363990, 389759189220, 2011540365174, 10381526171750, 53578887648690, 276519776741626, 1427114135562896

Offset: 1

R. H. Hardin, Oct 24 2014

nonn

Column 5 of A249290

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

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 87

Empirical recurrence of order 87 (see link above)

A249288 Number of length n+3 0..6 arrays with no four consecutive terms having the sum of any three elements equal to three times the fourth.

Original entry on oeis.org

2070, 12600, 76856, 469072, 2863158, 17477172, 106687006, 651265876, 3975630136, 24269116850, 148150208272, 904379542250, 5520764471064, 33701382275398, 205729331323368, 1255870097060206, 7666430906270386, 46799555928424622

Offset: 1

R. H. Hardin, Oct 24 2014

nonn

Column 6 of A249290

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

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

A249289 Number of length n+3 0..7 arrays with no four consecutive terms having the sum of any three elements equal to three times the fourth.

Original entry on oeis.org

3584, 25280, 178644, 1263044, 8930228, 63142432, 446465388, 3156873140, 22321652802, 157832259724, 1116002868810, 7891051581722, 55796177670214, 394524535750878, 2789610622867354, 19724825025520940, 139470619655277052

Offset: 1

R. H. Hardin, Oct 24 2014

nonn

Column 7 of A249290

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

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

A249291 Number of length 1+3 0..n arrays with no four consecutive terms having the sum of any three elements equal to three times the fourth.

Original entry on oeis.org

14, 66, 204, 524, 1098, 2070, 3584, 5808, 8934, 13202, 18828, 26100, 35306, 46758, 60792, 77792, 98118, 122202, 150476, 183396, 221442, 265142, 315000, 371592, 435494, 507306, 587652, 677204, 776610, 886590, 1007864, 1141176, 1287294

Offset: 1

R. H. Hardin, Oct 24 2014

nonn

			Some solutions for n=10:
  3  3  2  5  3  1  7  2  9  5  9  1  9  6  0  0
  3  7  0  9  5  7 10  0  8  9  2  5  5  7  1  5
  1  3  8 10  6  7  3  1  7  8  1  9  3  0  2  9
  1  1  4  6  0  3 10  9  0  2 10  8  4  4 10  1

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

Row 1 of A249290.

Empirical: a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + a(n-5) + 2*a(n-6) - 3*a(n-7) +a(n- 8).
Empirical for n mod 6 = 0: a(n) = n^4 + (8/3)*n^3 + 5*n^2 + 3*n
Empirical for n mod 6 = 1: a(n) = n^4 + (8/3)*n^3 + 5*n^2 + 3*n + (7/3)
Empirical for n mod 6 = 2: a(n) = n^4 + (8/3)*n^3 + 5*n^2 + 3*n + (8/3)
Empirical for n mod 6 = 3: a(n) = n^4 + (8/3)*n^3 + 5*n^2 + 3*n - 3
Empirical for n mod 6 = 4: a(n) = n^4 + (8/3)*n^3 + 5*n^2 + 3*n + (16/3)
Empirical for n mod 6 = 5: a(n) = n^4 + (8/3)*n^3 + 5*n^2 + 3*n - (1/3).
Empirical g.f.: 2*x*(7 + 12*x + 17*x^2 + 29*x^3 + 7*x^5) / ((1 - x)^5*(1 + x)*(1 + x + x^2)). - Colin Barker, Nov 09 2018

A249292 Number of length 2+3 0..n arrays with no four consecutive terms having the sum of any three elements equal to three times the fourth.

Original entry on oeis.org

26, 168, 660, 2228, 5646, 12600, 25280, 46608, 80334, 131672, 206112, 311352, 455954, 649920, 904884, 1235024, 1654734, 2181960, 2836016, 3638460, 4613010, 5786924, 7188012, 8848968, 10803998, 13090368, 15748356, 18822884, 22359246

Offset: 1

R. H. Hardin, Oct 24 2014

nonn

Row 2 of A249290

			Some solutions for n=10
..4....0....9....7....5....3....9....2....1....3....3....1....1....5....1....4
..7....3....7....5....3....2....5....5....5....2....7....7...10....6....6...10
..4....7....2...10...10....8....6....8....3....1....5...10....1....6....9....3
..3....1....1....8...10....2....5....9....6...10....3....5....9....6...10....6
..7....0....0....2....6....8....9....3....7....9....4....7....7....7....5....0

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

Empirical: a(n) = 2*a(n-1) -2*a(n-2) +2*a(n-3) -a(n-4) +a(n-5) -a(n-6) +a(n-8) -2*a(n-9) +a(n-10) -a(n-11) +a(n-12) -2*a(n-13) +2*a(n-14) +2*a(n-18) -2*a(n-19) +a(n-20) -a(n-21) +a(n-22) -2*a(n-23) +a(n-24) -a(n-26) +a(n-27) -a(n-28) +2*a(n-29) -2*a(n-30) +2*a(n-31) -a(n-32)
Also a polynomial of degree 5 plus a linear quasipolynomial with period 360, the first 12 being:
Empirical for n mod 360 = 0: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (107/10)*n
Empirical for n mod 360 = 1: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (967/60)*n - (113/60)
Empirical for n mod 360 = 2: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (481/30)*n + (8/15)
Empirical for n mod 360 = 3: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (49/20)*n - (3/4)
Empirical for n mod 360 = 4: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (641/30)*n - (26/15)
Empirical for n mod 360 = 5: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (647/60)*n - (125/12)
Empirical for n mod 360 = 6: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (107/10)*n - (114/5)
Empirical for n mod 360 = 7: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (787/60)*n - (653/60)
Empirical for n mod 360 = 8: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (481/30)*n - (20/3)
Empirical for n mod 360 = 9: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (109/20)*n + (117/20)
Empirical for n mod 360 = 10: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (641/30)*n + (20/3)
Empirical for n mod 360 = 11: a(n) = n^5 + (7/3)*n^4 + (97/12)*n^3 + (7/20)*n^2 + (467/60)*n + (707/60)

A249293 Number of length 3+3 0..n arrays with no four consecutive terms having the sum of any three elements equal to three times the fourth.

Original entry on oeis.org

48, 428, 2144, 9504, 29100, 76856, 178644, 374540, 723300, 1314744, 2258528, 3717444, 5893024, 9039940, 13477788, 19618656, 27921268, 38978528, 53474096, 72214004, 96133160, 126348344, 164077052, 210790324, 268108160, 337868944

Offset: 1

R. H. Hardin, Oct 24 2014

nonn

Row 3 of A249290

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

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

A249294 Number of length 4+3 0..n arrays with no four consecutive terms having the sum of any three elements equal to three times the fourth.

Original entry on oeis.org

88, 1094, 6960, 40588, 150112, 469072, 1263044, 3011088, 6514660, 13131956, 24755440, 44396112, 76182120, 125764540, 200780652, 311698092, 471201156, 696406084, 1008398272, 1433424724, 2003585272, 2758886876, 3745643452

Offset: 1

R. H. Hardin, Oct 24 2014

nonn

Row 4 of A249290.

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

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

Cf. A249290.

cp's OEIS Frontend

A249284 Number of length n+3 0..2 arrays with no four consecutive terms having the sum of any three elements equal to three times the fourth.

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A249285 Number of length n+3 0..3 arrays with no four consecutive terms having the sum of any three elements equal to three times the fourth.

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A249286 Number of length n+3 0..4 arrays with no four consecutive terms having the sum of any three elements equal to three times the fourth.

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A249287 Number of length n+3 0..5 arrays with no four consecutive terms having the sum of any three elements equal to three times the fourth.

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A249288 Number of length n+3 0..6 arrays with no four consecutive terms having the sum of any three elements equal to three times the fourth.

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A249289 Number of length n+3 0..7 arrays with no four consecutive terms having the sum of any three elements equal to three times the fourth.

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A249291 Number of length 1+3 0..n arrays with no four consecutive terms having the sum of any three elements equal to three times the fourth.

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A249292 Number of length 2+3 0..n arrays with no four consecutive terms having the sum of any three elements equal to three times the fourth.

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A249293 Number of length 3+3 0..n arrays with no four consecutive terms having the sum of any three elements equal to three times the fourth.

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A249294 Number of length 4+3 0..n arrays with no four consecutive terms having the sum of any three elements equal to three times the fourth.

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