A252177 -id:A252177 - cp's OEIS frontend

A252171 Number of length n+2 0..2 arrays with the sum of the maximum minus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

3, 49, 83, 369, 957, 3217, 9295, 28977, 86267, 262541, 787121, 2374869, 7129517, 21441049, 64366847, 193314809, 580205169, 1741524549, 5225949099, 15681813101, 47052271005, 141174409049, 423556062389, 1270747118001, 3812396126529

Offset: 1

R. H. Hardin, Dec 15 2014

nonn

Column 2 of A252177

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

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

Empirical: a(n) = 8*a(n-1) -21*a(n-2) +10*a(n-3) +54*a(n-4) -128*a(n-5) +125*a(n-6) -142*a(n-8) +176*a(n-9) -199*a(n-10) +216*a(n-11) -150*a(n-12) +80*a(n-13) -24*a(n-14)

A252172 Number of length n+2 0..3 arrays with the sum of the maximum minus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

4, 132, 264, 1872, 6820, 31420, 123826, 515268, 2058802, 8332796, 33350162, 133891940, 535789038, 2145632584, 8584207782, 34349419412, 137408677592, 549699224224, 2198863697876, 8795786194236, 35183533311476, 140735839290104

Offset: 1

R. H. Hardin, Dec 15 2014

nonn

Column 3 of A252177

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

R. H. Hardin, Table of n, a(n) for n = 1..129

Empirical: a(n) = 13*a(n-1) -60*a(n-2) +76*a(n-3) +310*a(n-4) -1328*a(n-5) +1601*a(n-6) +1043*a(n-7) -4739*a(n-8) +6283*a(n-9) -16535*a(n-10) +47913*a(n-11) -56399*a(n-12) -41587*a(n-13) +227738*a(n-14) -387264*a(n-15) +541852*a(n-16) -755788*a(n-17) +635056*a(n-18) +469432*a(n-19) -2549608*a(n-20) +5018568*a(n-21) -7394016*a(n-22) +8952448*a(n-23) -8287952*a(n-24) +4052560*a(n-25) +3641808*a(n-26) -12878128*a(n-27) +21320784*a(n-28) -27162288*a(n-29) +29035680*a(n-30) -26480832*a(n-31) +20563584*a(n-32) -13528064*a(n-33) +7524864*a(n-34) -3517952*a(n-35) +1345536*a(n-36) -396288*a(n-37) +79872*a(n-38) -8192*a(n-39) for n>40

A252173 Number of length n+2 0..4 arrays with the sum of the maximum minus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

5, 285, 687, 6361, 30315, 179225, 907249, 4728833, 23847033, 120644221, 605522767, 3038459385, 15215512685, 76167143089, 381063555999, 1906111738921, 9532798497759, 47671420448717, 238379347788679, 1191968945583273

Offset: 1

R. H. Hardin, Dec 15 2014

nonn

Column 4 of A252177

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

R. H. Hardin, Table of n, a(n) for n = 1..84

A252178 Number of length 2+2 0..n arrays with the sum of the maximum minus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

12, 49, 132, 285, 536, 917, 1464, 2217, 3220, 4521, 6172, 8229, 10752, 13805, 17456, 21777, 26844, 32737, 39540, 47341, 56232, 66309, 77672, 90425, 104676, 120537, 138124, 157557, 178960, 202461, 228192, 256289, 286892, 320145, 356196, 395197

Offset: 1

R. H. Hardin, Dec 15 2014

nonn

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

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

Row 2 of A252177.

Empirical: a(n) = (1/6)*n^4 + (7/3)*n^3 + (29/6)*n^2 + (11/3)*n + 1.
Conjectures from Colin Barker, Dec 01 2018: (Start)
G.f.: x*(12 - 11*x + 7*x^2 - 5*x^3 + x^4) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
(End)

A252179 Number of length 3+2 0..n arrays with the sum of the maximum minus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

12, 83, 264, 687, 1428, 2729, 4680, 7661, 11764, 17535, 25056, 35067, 47628, 63701, 83312, 107673, 136764, 172075, 213528, 262919, 320100, 387201, 463992, 552965, 653796, 769367, 899248, 1046739, 1211292, 1396653, 1602144, 1831985, 2085356

Offset: 1

R. H. Hardin, Dec 15 2014

nonn

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

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

Row 3 of A252177.

Empirical: a(n) = 3*a(n-1) - 8*a(n-3) + 6*a(n-4) + 6*a(n-5) - 8*a(n-6) + 3*a(n-8) - a(n-9).
Empirical for n mod 2 = 0: a(n) = (1/60)*n^5 + (17/16)*n^4 + (14/3)*n^3 + (11/2)*n^2 + (77/30)*n + 1.
Empirical for n mod 2 = 1: a(n) = (1/60)*n^5 + (17/16)*n^4 + (14/3)*n^3 + (39/8)*n^2 + (79/60)*n + (1/16).
Empirical g.f.: x*(12 + 47*x + 15*x^2 - 9*x^3 - 41*x^4 - 13*x^5 + 3*x^6 + 3*x^7 - x^8) / ((1 - x)^6*(1 + x)^3). - Colin Barker, Dec 01 2018

A252180 Number of length 4+2 0..n arrays with the sum of the maximum minus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

40, 369, 1872, 6361, 17092, 39109, 79672, 148673, 259248, 428045, 675436, 1027273, 1513112, 2169245, 3037220, 4166229, 5610160, 7435141, 9709732, 12516761, 15944392, 20095193, 25074784, 31012613, 38034620, 46293613, 55944576, 67167485

Offset: 1

R. H. Hardin, Dec 15 2014

nonn

Row 4 of A252177

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

R. H. Hardin, Table of n, a(n) for n = 1..94

Empirical: a(n) = -a(n-1) +a(n-2) +5*a(n-3) +6*a(n-4) -2*a(n-5) -12*a(n-6) -16*a(n-7) -3*a(n-8) +17*a(n-9) +25*a(n-10) +13*a(n-11) -13*a(n-12) -25*a(n-13) -17*a(n-14) +3*a(n-15) +16*a(n-16) +12*a(n-17) +2*a(n-18) -6*a(n-19) -5*a(n-20) -a(n-21) +a(n-22) +a(n-23)
Empirical for n mod 12 = 0: a(n) = (1/60)*n^6 + (40169/12960)*n^5 + (46981/5184)*n^4 + (12695/1296)*n^3 + (3389/360)*n^2 + (409/90)*n + 1
Empirical for n mod 12 = 1: a(n) = (1/60)*n^6 + (40169/12960)*n^5 + (46981/5184)*n^4 + (6253/648)*n^3 + (132259/12960)*n^2 + (91631/12960)*n + (4645/5184)
Empirical for n mod 12 = 2: a(n) = (1/60)*n^6 + (40169/12960)*n^5 + (46981/5184)*n^4 + (12631/1296)*n^3 + (30341/3240)*n^2 + (6647/1620)*n + (37/324)
Empirical for n mod 12 = 3: a(n) = (1/60)*n^6 + (40169/12960)*n^5 + (46981/5184)*n^4 + (6253/648)*n^3 + (14411/1440)*n^2 + (10039/1440)*n + (69/64)
Empirical for n mod 12 = 4: a(n) = (1/60)*n^6 + (40169/12960)*n^5 + (46981/5184)*n^4 + (12695/1296)*n^3 + (31141/3240)*n^2 + (3761/810)*n - (35/81)
Empirical for n mod 12 = 5: a(n) = (1/60)*n^6 + (40169/12960)*n^5 + (46981/5184)*n^4 + (6221/648)*n^3 + (129059/12960)*n^2 + (81391/12960)*n + (6181/5184)
Empirical for n mod 12 = 6: a(n) = (1/60)*n^6 + (40169/12960)*n^5 + (46981/5184)*n^4 + (12695/1296)*n^3 + (3389/360)*n^2 + (863/180)*n + (5/4)
Empirical for n mod 12 = 7: a(n) = (1/60)*n^6 + (40169/12960)*n^5 + (46981/5184)*n^4 + (6253/648)*n^3 + (132259/12960)*n^2 + (91631/12960)*n - (1835/5184)
Empirical for n mod 12 = 8: a(n) = (1/60)*n^6 + (40169/12960)*n^5 + (46981/5184)*n^4 + (12631/1296)*n^3 + (30341/3240)*n^2 + (3121/810)*n - (11/81)
Empirical for n mod 12 = 9: a(n) = (1/60)*n^6 + (40169/12960)*n^5 + (46981/5184)*n^4 + (6253/648)*n^3 + (14411/1440)*n^2 + (10039/1440)*n + (149/64)
Empirical for n mod 12 = 10: a(n) = (1/60)*n^6 + (40169/12960)*n^5 + (46981/5184)*n^4 + (12695/1296)*n^3 + (31141/3240)*n^2 + (7927/1620)*n - (59/324)
Empirical for n mod 12 = 11: a(n) = (1/60)*n^6 + (40169/12960)*n^5 + (46981/5184)*n^4 + (6221/648)*n^3 + (129059/12960)*n^2 + (81391/12960)*n - (299/5184)

A252181 Number of length 5+2 0..n arrays with the sum of the maximum minus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

56, 957, 6820, 30315, 100894, 277101, 654644, 1397115, 2729346, 5000775, 8646710, 14320677, 22753218, 35050107, 52358558, 76391397, 108844088, 152265601, 208998994, 282689603, 376505412, 495411841, 643581780, 827671511, 1052928232

Offset: 1

R. H. Hardin, Dec 15 2014

nonn

Row 5 of A252177

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

R. H. Hardin, Table of n, a(n) for n = 1..34

A252174 Number of length n+2 0..5 arrays with the sum of the maximum minus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

6, 536, 1428, 17092, 100894, 753200, 4652710, 29364176, 177955614, 1080135428, 6499878776, 39104150100, 234816782208, 1409805025568, 8460732943882, 50772490924064, 304654183120186, 1828001400070884, 10968208935015636

Offset: 1

R. H. Hardin, Dec 15 2014

nonn

Column 5 of A252177

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

A252175 Number of length n+2 0..6 arrays with the sum of the maximum minus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

7, 917, 2729, 39109, 277101, 2485637, 18231947, 135424961, 963247737, 6838373877, 48103629141, 337900112109, 2368821073603, 16597473994629, 116236940081089

Offset: 1

R. H. Hardin, Dec 15 2014

nonn

Column 6 of A252177

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

A252176 Number of length n+2 0..7 arrays with the sum of the maximum minus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

8, 1464, 4680, 79672, 654644, 6994984, 59838132, 513937352, 4190189694, 34020988396, 273415166334, 2193948803940

Offset: 1

R. H. Hardin, Dec 15 2014

nonn

Column 7 of A252177

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

cp's OEIS Frontend

A252171 Number of length n+2 0..2 arrays with the sum of the maximum minus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

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A252172 Number of length n+2 0..3 arrays with the sum of the maximum minus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

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A252173 Number of length n+2 0..4 arrays with the sum of the maximum minus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

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A252178 Number of length 2+2 0..n arrays with the sum of the maximum minus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

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A252179 Number of length 3+2 0..n arrays with the sum of the maximum minus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

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A252180 Number of length 4+2 0..n arrays with the sum of the maximum minus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

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A252181 Number of length 5+2 0..n arrays with the sum of the maximum minus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

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A252174 Number of length n+2 0..5 arrays with the sum of the maximum minus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

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A252175 Number of length n+2 0..6 arrays with the sum of the maximum minus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

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A252176 Number of length n+2 0..7 arrays with the sum of the maximum minus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.

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