A250419 -id:A250419 - cp's OEIS frontend

A250413 Number of length n+1 0..2 arrays with the sum of the minimum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

5, 17, 38, 125, 335, 1061, 3069, 9495, 28221, 86149, 258252, 782393, 2350442, 7090347, 21303611, 64109181, 192553620, 578665211, 1737374865, 5217197093, 15659477401, 47004010481, 141055441813, 423295193635, 1270118805510

Offset: 1

R. H. Hardin, Nov 22 2014

nonn

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

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

Column 2 of A250419.

Empirical: a(n) = 6*a(n-1) - 3*a(n-2) - 40*a(n-3) + 59*a(n-4) + 68*a(n-5) - 146*a(n-6) - 14*a(n-7) + 91*a(n-8) - 8*a(n-9) - 12*a(n-10).

Empirical g.f.: x*(5 - 13*x - 49*x^2 + 148*x^3 + 84*x^4 - 397*x^5 + 40*x^6 + 257*x^7 - 36*x^8 - 36*x^9) / ((1 - x)*(1 - 2*x)*(1 + 2*x)*(1 - 3*x)*(1 - 2*x - x^2 + x^3)*(1 - 3*x^2 - x^3)). - Colin Barker, Nov 14 2018

A250414 Number of length n+1 0..3 arrays with the sum of the minimum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

7, 36, 99, 476, 1693, 7504, 29221, 123242, 492076, 2021436, 8111306, 32877666, 131905733, 531080990, 2128576994, 8541648896, 34206851593, 137042168870, 548526597108, 2195788650322, 8786230110165, 35158099104398, 140658315422311

Offset: 1

R. H. Hardin, Nov 22 2014

nonn

Column 3 of A250419

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

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

Empirical: a(n) = 12*a(n-1) -23*a(n-2) -252*a(n-3) +1056*a(n-4) +1766*a(n-5) -14214*a(n-6) -1040*a(n-7) +103693*a(n-8) -58064*a(n-9) -484016*a(n-10) +411280*a(n-11) +1566651*a(n-12) -1472256*a(n-13) -3670072*a(n-14) +3223960*a(n-15) +6306524*a(n-16) -4463544*a(n-17) -7823016*a(n-18) +3799616*a(n-19) +6723120*a(n-20) -1817056*a(n-21) -3791856*a(n-22) +352032*a(n-23) +1315312*a(n-24) +57408*a(n-25) -252160*a(n-26) -37120*a(n-27) +20352*a(n-28) +4608*a(n-29)

A250415 Number of length n+1 0..4 arrays with the sum of the minimum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

9, 65, 205, 1351, 5982, 34415, 169352, 904695, 4547008, 23448029, 117953499, 598260521, 3002881031, 15113176921, 75724031785, 379750748041, 1900758538693, 9516621521809, 47607635835257, 238183334181909, 1191212059701364

Offset: 1

R. H. Hardin, Nov 22 2014

nonn

Column 4 of A250419

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

R. H. Hardin, Table of n, a(n) for n = 1..91

A250416 Number of length n+1 0..5 arrays with the sum of the minimum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

11, 106, 370, 3154, 16790, 119364, 713260, 4620694, 28033122, 174036890, 1052524169, 6409923762, 38618278972, 233193985046, 1401840843777, 8433815453844, 50645668891739, 304220519953548, 1825994803261130

Offset: 1

R. H. Hardin, Nov 22 2014

nonn

Column 5 of A250419

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

R. H. Hardin, Table of n, a(n) for n = 1..47

A250417 Number of length n+1 0..6 arrays with the sum of the minimum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

13, 161, 606, 6433, 39916, 341011, 2399000, 18334295, 130350889, 947356115, 6693133584, 47588393713, 334543874696, 2356688545513, 16526137384381, 115977271626785, 812415242570854, 5692700008978435, 39860063264311589

Offset: 1

R. H. Hardin, Nov 22 2014

nonn

Column 6 of A250419

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

R. H. Hardin, Table of n, a(n) for n = 1..38

A250418 Number of length n+1 0..7 arrays with the sum of the minimum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

15, 232, 927, 11906, 84094, 845358, 6847916, 60473968, 493271080, 4110606460, 33227112639, 270174922792, 2170847791630, 17476736034672, 140045328565480, 1123079823815258, 8990031255733660, 71987420633900826, 576024775450468215

Offset: 1

R. H. Hardin, Nov 22 2014

nonn

Column 7 of A250419

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

R. H. Hardin, Table of n, a(n) for n = 1..23

A250420 Number of length 3+1 0..n arrays with the sum of the minimum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

10, 38, 99, 205, 370, 606, 927, 1345, 1874, 2526, 3315, 4253, 5354, 6630, 8095, 9761, 11642, 13750, 16099, 18701, 21570, 24718, 28159, 31905, 35970, 40366, 45107, 50205, 55674, 61526, 67775, 74433, 81514, 89030, 96995, 105421, 114322, 123710, 133599

Offset: 1

R. H. Hardin, Nov 22 2014

nonn

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

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

Row 3 of A250419.

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 2 = 0: a(n) = (13/6)*n^3 + (13/4)*n^2 + (10/3)*n + 1.
Empirical for n mod 2 = 1: a(n) = (13/6)*n^3 + (13/4)*n^2 + (10/3)*n + (5/4).
Empirical g.f.: x*(10 + 8*x + 5*x^2 + 4*x^3 - x^4) / ((1 - x)^4*(1 + x)). - Colin Barker, Nov 14 2018

A250421 Number of length 4+1 0..n arrays with the sum of the minimum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

20, 125, 476, 1351, 3154, 6433, 11906, 20461, 33178, 51359, 76520, 110417, 155080, 212797, 286144, 378023, 491638, 630529, 798614, 1000157, 1239806, 1522639, 1854124, 2240161, 2687132, 3201853, 3791620, 4464263, 5228090, 6091937, 7065226

Offset: 1

R. H. Hardin, Nov 22 2014

nonn

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

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

Row 4 of A250419.

Empirical: a(n) = 4*a(n-1) - 6*a(n-2) + 6*a(n-3) - 9*a(n-4) + 12*a(n-5) - 9*a(n-6) + 6*a(n-7) - 6*a(n-8) + 4*a(n-9) - a(n-10).
Empirical for n mod 3 = 0: a(n) = (2/15)*n^5 + (92/27)*n^4 + (85/27)*n^3 + (68/9)*n^2 + (68/15)*n + 1.
Empirical for n mod 3 = 1: a(n) = (2/15)*n^5 + (92/27)*n^4 + (85/27)*n^3 + (68/9)*n^2 + (632/135)*n + (29/27).
Empirical for n mod 3 = 2: a(n) = (2/15)*n^5 + (92/27)*n^4 + (85/27)*n^3 + (68/9)*n^2 + (652/135)*n + (31/27).
Empirical g.f.: x*(20 + 45*x + 96*x^2 + 77*x^3 + 36*x^4 - 48*x^5 - 44*x^6 - 37*x^7 - x^9) / ((1 - x)^6*(1 + x + x^2)^2). - Colin Barker, Nov 14 2018

A250422 Number of length 5+1 0..n arrays with the sum of the minimum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

36, 335, 1693, 5982, 16790, 39916, 84094, 161350, 287910, 484353, 776742, 1196504, 1781894, 2577507, 3636138, 5017850, 6792317, 9037401, 11842016, 15304097, 19534144, 24652517, 30793639, 38102572, 46740025, 56878092, 68706116, 82425513

Offset: 1

R. H. Hardin, Nov 22 2014

nonn

Row 5 of A250419

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

R. H. Hardin, Table of n, a(n) for n = 1..206

Empirical: a(n) = a(n-1) +a(n-2) +a(n-3) -4*a(n-5) -a(n-6) -a(n-7) +4*a(n-8) +4*a(n-9) -a(n-10) -a(n-11) -4*a(n-12) +a(n-14) +a(n-15) +a(n-16) -a(n-17)
Empirical for n mod 12 = 0: a(n) = (16771/3456)*n^5 - (18673/6912)*n^4 + (133891/5184)*n^3 + (689/288)*n^2 + (211/72)*n + 1
Empirical for n mod 12 = 1: a(n) = (16771/3456)*n^5 - (18673/6912)*n^4 + (133891/5184)*n^3 + (3449/1152)*n^2 + (4903/3456)*n + (74825/20736)
Empirical for n mod 12 = 2: a(n) = (16771/3456)*n^5 - (18673/6912)*n^4 + (133891/5184)*n^3 + (689/288)*n^2 + (395/144)*n + (1633/1296)
Empirical for n mod 12 = 3: a(n) = (16771/3456)*n^5 - (18673/6912)*n^4 + (133891/5184)*n^3 + (3449/1152)*n^2 + (1765/1152)*n + (953/256)
Empirical for n mod 12 = 4: a(n) = (16771/3456)*n^5 - (18673/6912)*n^4 + (133891/5184)*n^3 + (689/288)*n^2 + (649/216)*n + (92/81)
Empirical for n mod 12 = 5: a(n) = (16771/3456)*n^5 - (18673/6912)*n^4 + (133891/5184)*n^3 + (3449/1152)*n^2 + (1549/1152)*n + (76105/20736)
Empirical for n mod 12 = 6: a(n) = (16771/3456)*n^5 - (18673/6912)*n^4 + (133891/5184)*n^3 + (689/288)*n^2 + (395/144)*n + (17/16)
Empirical for n mod 12 = 7: a(n) = (16771/3456)*n^5 - (18673/6912)*n^4 + (133891/5184)*n^3 + (3449/1152)*n^2 + (5551/3456)*n + (80009/20736)
Empirical for n mod 12 = 8: a(n) = (16771/3456)*n^5 - (18673/6912)*n^4 + (133891/5184)*n^3 + (689/288)*n^2 + (211/72)*n + (97/81)
Empirical for n mod 12 = 9: a(n) = (16771/3456)*n^5 - (18673/6912)*n^4 + (133891/5184)*n^3 + (3449/1152)*n^2 + (1549/1152)*n + (889/256)
Empirical for n mod 12 = 10: a(n) = (16771/3456)*n^5 - (18673/6912)*n^4 + (133891/5184)*n^3 + (689/288)*n^2 + (1217/432)*n + (1553/1296)
Empirical for n mod 12 = 11: a(n) = (16771/3456)*n^5 - (18673/6912)*n^4 + (133891/5184)*n^3 + (3449/1152)*n^2 + (1765/1152)*n + (81289/20736)

A250423 Number of length 6+1 0..n arrays with the sum of the minimum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

72, 1061, 7504, 34415, 119364, 341011, 845358, 1878315, 3826222, 7263401, 13006830, 22184249, 36304264, 57333585, 87793296, 130863267, 190475904, 271446215, 379605094, 521929211, 706693318, 943642869, 1244141718, 1621385877

Offset: 1

R. H. Hardin, Nov 22 2014

nonn

Row 6 of A250419

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

R. H. Hardin, Table of n, a(n) for n = 1..55

cp's OEIS Frontend

A250413 Number of length n+1 0..2 arrays with the sum of the minimum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

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A250414 Number of length n+1 0..3 arrays with the sum of the minimum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

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A250415 Number of length n+1 0..4 arrays with the sum of the minimum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

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A250416 Number of length n+1 0..5 arrays with the sum of the minimum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

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A250417 Number of length n+1 0..6 arrays with the sum of the minimum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

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A250418 Number of length n+1 0..7 arrays with the sum of the minimum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

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A250420 Number of length 3+1 0..n arrays with the sum of the minimum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

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A250421 Number of length 4+1 0..n arrays with the sum of the minimum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

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A250422 Number of length 5+1 0..n arrays with the sum of the minimum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

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A250423 Number of length 6+1 0..n arrays with the sum of the minimum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

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