A248461 -id:A248461 - cp's OEIS frontend

A248456 Number of length n+2 0..3 arrays with no three consecutive terms having the sum of any two elements equal to twice the third.

48, 148, 460, 1436, 4488, 14040, 43940, 137532, 430508, 1347652, 4218704, 13206360, 41341772, 129418260, 405137308, 1268262348, 3970233208, 12428621208, 38907193300, 121797075276, 381279818252, 1193577924020, 3736437636672

Offset: 1

R. H. Hardin, Oct 06 2014

nonn

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

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

Column 3 of A248461.

Empirical: a(n) = 2*a(n-1) + 3*a(n-2) + 4*a(n-3) - 3*a(n-4) - 12*a(n-5) - 4*a(n-6).

Empirical g.f.: 4*x*(12 + 13*x + 5*x^2 - 30*x^3 - 53*x^4 - 16*x^5) / (1 - 2*x - 3*x^2 - 4*x^3 + 3*x^4 + 12*x^5 + 4*x^6). - Colin Barker, Nov 08 2018

A248457 Number of length n+2 0..4 arrays with no three consecutive terms having the sum of any two elements equal to twice the third.

Original entry on oeis.org

96, 380, 1512, 6040, 24160, 96736, 387488, 1552448, 6220480, 24926080, 99883840, 400260160, 1603955712, 6427525312, 25757039296, 103216337152, 413619611968, 1657501354048, 6642119813120, 26617026736320, 106662654436544

Offset: 1

R. H. Hardin, Oct 06 2014

nonn

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

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

Column 4 of A248461.

Empirical: a(n) = 3*a(n-1) + 5*a(n-2) + 2*a(n-3) - 16*a(n-4) - 28*a(n-5) - 8*a(n-6).

Empirical g.f.: 4*x*(24 + 23*x - 27*x^2 - 147*x^3 - 186*x^4 - 50*x^5) / ((1 - 2*x)*(1 - x - 7*x^2 - 16*x^3 - 16*x^4 - 4*x^5)). - Colin Barker, Nov 08 2018

A248458 Number of length n+2 0..5 arrays with no three consecutive terms having the sum of any two elements equal to twice the third.

Original entry on oeis.org

174, 862, 4272, 21182, 105026, 520788, 2582406, 12805334, 63497776, 314866606, 1561330890, 7742183252, 38391228334, 190370917646, 943993962960, 4680991358518, 23211674211122, 115099939580084, 570747116572614

Offset: 1

R. H. Hardin, Oct 06 2014

nonn

Column 5 of A248461

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

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

Empirical: a(n) = 3*a(n-1) +10*a(n-2) +11*a(n-3) -32*a(n-4) -119*a(n-5) -139*a(n-6) -26*a(n-7) +126*a(n-8) +130*a(n-9) +28*a(n-10) -12*a(n-11) -4*a(n-12)

A248459 Number of length n+2 0..6 arrays with no three consecutive terms having the sum of any two elements equal to twice the third.

Original entry on oeis.org

282, 1652, 9684, 56782, 332940, 1952254, 11447368, 67123652, 393591402, 2307892826, 13532738130, 79351606012, 465292191408, 2728323147524, 15998005845580, 93807139848202, 550054773800480, 3225343557770222

Offset: 1

R. H. Hardin, Oct 06 2014

nonn

Column 6 of A248461

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

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

Empirical: a(n) = 5*a(n-1) +4*a(n-2) +20*a(n-3) -58*a(n-4) -109*a(n-5) -155*a(n-6) +28*a(n-7) +295*a(n-8) +175*a(n-9) +153*a(n-10) +36*a(n-11) +382*a(n-12) +183*a(n-13) -193*a(n-14) +140*a(n-15) +96*a(n-16)

A248460 Number of length n+2 0..7 arrays with no three consecutive terms having the sum of any two elements equal to twice the third.

Original entry on oeis.org

432, 2956, 20236, 138534, 948412, 6493036, 44452660, 304332258, 2083523194, 14264241960, 97656029050, 668573914642, 4577199017242, 31336476646048, 214536174915418, 1468760220688680, 10055444434320028, 68841708367472026

Offset: 1

R. H. Hardin, Oct 06 2014

nonn

Column 7 of A248461

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

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

Empirical: a(n) = 6*a(n-1) +9*a(n-2) -2*a(n-3) -109*a(n-4) -203*a(n-5) -4*a(n-6) +520*a(n-7) +1012*a(n-8) +696*a(n-9) +385*a(n-10) +373*a(n-11) -514*a(n-12) -2737*a(n-13) -4627*a(n-14) -3396*a(n-15) -2854*a(n-16) -3670*a(n-17) -2204*a(n-18) -634*a(n-19) -332*a(n-20) -162*a(n-21) -24*a(n-22)

A248462 Number of length 1+2 0..n arrays with no three consecutive terms having the sum of any two elements equal to twice the third.

Original entry on oeis.org

6, 18, 48, 96, 174, 282, 432, 624, 870, 1170, 1536, 1968, 2478, 3066, 3744, 4512, 5382, 6354, 7440, 8640, 9966, 11418, 13008, 14736, 16614, 18642, 20832, 23184, 25710, 28410, 31296, 34368, 37638, 41106, 44784, 48672, 52782, 57114, 61680, 66480, 71526

Offset: 1

R. H. Hardin, Oct 06 2014

nonn

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

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

Row 1 of A248461.

Empirical: a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +3*a(n-4) -a(n-5).
Empirical for n mod 12 = 0: a(n) = n^3 + (3/2)*n^2 + 2*n.
Empirical for n mod 12 = 1: a(n) = n^3 + (3/2)*n^2 + 2*n + (3/2).
Empirical g.f.: 6*x*(1 + x^2) / ((1 - x)^4*(1 + x)). - Colin Barker, Nov 08 2018

A248463 Number of length 2+2 0..n arrays with no three consecutive terms having the sum of any two elements equal to twice the third.

Original entry on oeis.org

10, 36, 148, 380, 862, 1652, 2956, 4860, 7642, 11400, 16488, 23044, 31482, 41952, 54956, 70672, 89662, 112128, 138708, 169632, 205610, 246884, 294240, 347960, 408890, 477324, 554196, 639828, 735214, 840700, 957356, 1085556, 1226442

Offset: 1

R. H. Hardin, Oct 06 2014

nonn

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

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

Row 2 of A248461.

Empirical: a(n) = 2*a(n-1) - a(n-3) - 2*a(n-5) + 2*a(n-6) + a(n-8) - 2*a(n-10) + a(n-11).
Empirical for n mod 12 = 0: a(n) = n^4 + n^3 + (25/6)*n^2 - (5/3)*n.
Empirical for n mod 12 = 1: a(n) = n^4 + n^3 + (25/6)*n^2 + (4/3)*n + (5/2).
Empirical for n mod 12 = 2: a(n) = n^4 + n^3 + (25/6)*n^2 - (5/3)*n - (4/3).
Empirical for n mod 12 = 3: a(n) = n^4 + n^3 + (25/6)*n^2 + (4/3)*n - (3/2).
Empirical for n mod 12 = 4: a(n) = n^4 + n^3 + (25/6)*n^2 - (5/3)*n.
Empirical for n mod 12 = 5: a(n) = n^4 + n^3 + (25/6)*n^2 + (4/3)*n + (7/6).
Empirical for n mod 12 = 6: a(n) = n^4 + n^3 + (25/6)*n^2 - (5/3)*n.
Empirical for n mod 12 = 7: a(n) = n^4 + n^3 + (25/6)*n^2 + (4/3)*n - (3/2).
Empirical for n mod 12 = 8: a(n) = n^4 + n^3 + (25/6)*n^2 - (5/3)*n - (4/3).
Empirical for n mod 12 = 9: a(n) = n^4 + n^3 + (25/6)*n^2 + (4/3)*n + (5/2).
Empirical for n mod 12 = 10: a(n) = n^4 + n^3 + (25/6)*n^2 - (5/3)*n.
Empirical for n mod 12 = 11: a(n) = n^4 + n^3 + (25/6)*n^2 + (4/3)*n - (17/6).
Empirical g.f.: 2*x*(5 + 8*x + 38*x^2 + 47*x^3 + 69*x^4 + 48*x^5 + 42*x^6 + 17*x^7 + 14*x^8) / ((1 - x)^5*(1 + x)^2*(1 + x^2)*(1 + x + x^2)). - Colin Barker, Nov 08 2018

A248464 Number of length 3+2 0..n arrays with no three consecutive terms having the sum of any two elements equal to twice the third.

Original entry on oeis.org

16, 72, 460, 1512, 4272, 9684, 20236, 37868, 67140, 111104, 177024, 269892, 400040, 574140, 806808, 1107132, 1493952, 1978984, 2586340, 3330852, 4242444, 5338788, 6656352, 8217136, 10064140, 12222784, 14744480, 17659176, 21025952, 24879392

Offset: 1

R. H. Hardin, Oct 06 2014

nonn

Row 3 of A248461

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

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

Empirical: a(n) = a(n-1) +a(n-3) -2*a(n-7) +a(n-8) -2*a(n-9) +a(n-10) -a(n-11) +2*a(n-12) +2*a(n-15) -a(n-16) +a(n-17) -2*a(n-18) +a(n-19) -2*a(n-20) +a(n-24) +a(n-26) -a(n-27)
Also a polynomial of degree 5 plus a quadratic quasipolynomial with period 840, the first 12 being:
Empirical for n mod 840 = 0: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (197/30)*n^2 + (51/5)*n
Empirical for n mod 840 = 1: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (31/15)*n^2 + (66/5)*n - (33/10)
Empirical for n mod 840 = 2: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (197/30)*n^2 + (113/15)*n - (152/15)
Empirical for n mod 840 = 3: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (31/15)*n^2 + (26/5)*n - (1/2)
Empirical for n mod 840 = 4: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (197/30)*n^2 + (51/5)*n - (12/5)
Empirical for n mod 840 = 5: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (31/15)*n^2 + (158/15)*n + (1/6)
Empirical for n mod 840 = 6: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (197/30)*n^2 + (51/5)*n - (24/5)
Empirical for n mod 840 = 7: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (31/15)*n^2 + (26/5)*n + (67/10)
Empirical for n mod 840 = 8: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (197/30)*n^2 + (113/15)*n - (4/3)
Empirical for n mod 840 = 9: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (31/15)*n^2 + (66/5)*n - (9/10)
Empirical for n mod 840 = 10: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (197/30)*n^2 + (51/5)*n - 8
Empirical for n mod 840 = 11: a(n) = n^5 + (1/2)*n^4 + (20/3)*n^3 - (31/15)*n^2 + (38/15)*n + (41/30)

A248465 Number of length 4+2 0..n arrays with no three consecutive terms having the sum of any two elements equal to twice the third.

Original entry on oeis.org

26, 144, 1436, 6040, 21182, 56782, 138534, 295078, 589916, 1082878, 1900666, 3161064, 5083368, 7857546, 11844802, 17344202, 24892396, 34927864, 48224830, 65403924, 87536430, 115449764, 150581308, 194049230, 247712034, 312987618

Offset: 1

R. H. Hardin, Oct 06 2014

nonn

Row 4 of A248461

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

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

Empirical: a(n) = -a(n-1) -a(n-2) +2*a(n-5) +3*a(n-6) +4*a(n-7) +3*a(n-8) +2*a(n-9) -3*a(n-11) -4*a(n-12) -6*a(n-13) -5*a(n-14) -5*a(n-15) +3*a(n-18) +2*a(n-19) +4*a(n-20) +a(n-21) -a(n-23) +2*a(n-25) +2*a(n-26) +5*a(n-27) +3*a(n-28) +5*a(n-29) -5*a(n-32) -3*a(n-33) -5*a(n-34) -2*a(n-35) -2*a(n-36) +a(n-38) -a(n-40) -4*a(n-41) -2*a(n-42) -3*a(n-43) +5*a(n-46) +5*a(n-47) +6*a(n-48) +4*a(n-49) +3*a(n-50) -2*a(n-52) -3*a(n-53) -4*a(n-54) -3*a(n-55) -2*a(n-56) +a(n-59) +a(n-60) +a(n-61)

A248466 Number of length 5+2 0..n arrays with no three consecutive terms having the sum of any two elements equal to twice the third.

Original entry on oeis.org

42, 288, 4488, 24160, 105026, 332940, 948412, 2299356, 5183202, 10554328, 20406996, 37023484, 64595054, 107536496, 173894220, 271712160, 414759462, 616455068, 899198128, 1284256968, 1806180638, 2496566424, 3406477720

Offset: 1

R. H. Hardin, Oct 06 2014

nonn

Row 5 of A248461

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

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

cp's OEIS Frontend

A248456 Number of length n+2 0..3 arrays with no three consecutive terms having the sum of any two elements equal to twice the third.

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A248457 Number of length n+2 0..4 arrays with no three consecutive terms having the sum of any two elements equal to twice the third.

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A248458 Number of length n+2 0..5 arrays with no three consecutive terms having the sum of any two elements equal to twice the third.

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A248459 Number of length n+2 0..6 arrays with no three consecutive terms having the sum of any two elements equal to twice the third.

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A248460 Number of length n+2 0..7 arrays with no three consecutive terms having the sum of any two elements equal to twice the third.

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A248462 Number of length 1+2 0..n arrays with no three consecutive terms having the sum of any two elements equal to twice the third.

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A248463 Number of length 2+2 0..n arrays with no three consecutive terms having the sum of any two elements equal to twice the third.

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A248464 Number of length 3+2 0..n arrays with no three consecutive terms having the sum of any two elements equal to twice the third.

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A248465 Number of length 4+2 0..n arrays with no three consecutive terms having the sum of any two elements equal to twice the third.

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A248466 Number of length 5+2 0..n arrays with no three consecutive terms having the sum of any two elements equal to twice the third.

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