A250646 -id:A250646 - cp's OEIS frontend

A250640 Number of length n+1 0..2 arrays with the sum of the maximum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

1, 17, 23, 125, 280, 1061, 2870, 9495, 27507, 86149, 255704, 782393, 2341381, 7090347, 21271463, 64109181, 192439733, 578665211, 1736971814, 5217197093, 15658051930, 47004010481, 141050402559, 423295193635, 1270100996174

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

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

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

Column 2 of A250646.

Empirical: a(n) = 6*a(n-1) - 3*a(n-2) - 42*a(n-3) + 71*a(n-4) + 56*a(n-5) - 192*a(n-6) + 80*a(n-7) + 77*a(n-8) - 64*a(n-9) + 12*a(n-10).

Empirical g.f.: x*(1 + 11*x - 76*x^2 + 80*x^3 + 242*x^4 - 541*x^5 + 201*x^6 + 239*x^7 - 192*x^8 + 36*x^9) / ((1 - x)*(1 - 2*x)*(1 + 2*x)*(1 - 3*x)*(1 - 3*x^2 + x^3)*(1 - 2*x - x^2 + x^3)). - Colin Barker, Nov 15 2018

A250641 Number of length n+1 0..3 arrays with the sum of the maximum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

1, 36, 44, 476, 1424, 7696, 28238, 126482, 491943, 2059700, 8161068, 33268124, 132637221, 534771362, 2136620867, 8574987528, 34285733053, 137334914170, 549255340746, 2198311980408, 8792729559738, 35179581032056, 140715004320059

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

Column 3 of A250646

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

R. H. Hardin, Table of n, a(n) for n = 1..187

Empirical: a(n) = 11*a(n-1) -22*a(n-2) -172*a(n-3) +787*a(n-4) +353*a(n-5) -7413*a(n-6) +8289*a(n-7) +29140*a(n-8) -67796*a(n-9) -32276*a(n-10) +217716*a(n-11) -108368*a(n-12) -314968*a(n-13) +384528*a(n-14) +123824*a(n-15) -451104*a(n-16) +169760*a(n-17) +185424*a(n-18) -183216*a(n-19) +24640*a(n-20) +40064*a(n-21) -24448*a(n-22) +5760*a(n-23) -512*a(n-24) for n>25

A250642 Number of length n+1 0..4 arrays with the sum of the maximum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

1, 65, 89, 1293, 4853, 34441, 163043, 915663, 4537317, 23671551, 118358549, 601565301, 3011330309, 15155615651, 75845220727, 380253505733, 1902264449049, 9522274036139, 47624961772074, 238244610944161, 1191402062810086

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

Column 4 of A250646

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

R. H. Hardin, Table of n, a(n) for n = 1..110

A250643 Number of length n+1 0..5 arrays with the sum of the maximum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

1, 106, 134, 2954, 12473, 120114, 677505, 4749950, 28200435, 177863786, 1063874048, 6491819162, 38892883673, 234724691398, 1407192408230, 8460554956974, 50741165814612, 304671802762820, 1827631230875303

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

Column 5 of A250646

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

R. H. Hardin, Table of n, a(n) for n = 1..40

A250644 Number of length n+1 0..6 arrays with the sum of the maximum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

1, 161, 219, 5901, 28379, 332827, 2225195, 18399217, 129137886, 953809557, 6704767056, 47777146765, 335147823244, 2360792885729, 16540740396740, 116054610957529, 812699929957712, 5694036707961181, 39865043590813086

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

Column 6 of A250646.

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

R. H. Hardin, Table of n, a(n) for n = 1..25

Cf. A250646.

A250647 Number of length 3+1 0..n arrays with the sum of the maximum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

6, 23, 44, 89, 134, 219, 296, 433, 550, 751, 916, 1193, 1414, 1779, 2064, 2529, 2886, 3463, 3900, 4601, 5126, 5963, 6584, 7569, 8294, 9439, 10276, 11593, 12550, 14051, 15136, 16833, 18054, 19959, 21324, 23449, 24966, 27323, 29000, 31601, 33446, 36303

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

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

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

Row 3 of A250646.

Empirical: a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) - 3*a(n-4) + 3*a(n-5) + a(n-6) - a(n-7).
Empirical for n mod 2 = 0: a(n) = (5/12)*n^3 + 3*n^2 + (10/3)*n + 1.
Empirical for n mod 2 = 1: a(n) = (5/12)*n^3 + (11/4)*n^2 + (31/12)*n + (1/4).
Empirical g.f.: x*(6 + 17*x + 3*x^2 - 6*x^3 + x^5 - x^6) / ((1 - x)^4*(1 + x)^3). - Colin Barker, Nov 15 2018

A250648 Number of length 4+1 0..n arrays with the sum of the maximum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

20, 125, 476, 1293, 2954, 5901, 10766, 18305, 29478, 45361, 67364, 96961, 135976, 186445, 250688, 331213, 431054, 553277, 701474, 879553, 1091754, 1342593, 1637320, 1981153, 2380028, 2840317, 3368740, 3972397, 4659346, 5437517, 6315766

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

Row 4 of A250646.

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

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

Cf. A250646.

Empirical: a(n) = a(n-1) +2*a(n-2) +a(n-3) -4*a(n-4) -5*a(n-5) +3*a(n-6) +6*a(n-7) +3*a(n-8) -5*a(n-9) -4*a(n-10) +a(n-11) +2*a(n-12) +a(n-13) -a(n-14).
Empirical for n mod 6 = 0: a(n) = (2/15)*n^5 + (403/162)*n^4 + (532/81)*n^3 + (17/3)*n^2 + (124/45)*n + 1.
Empirical for n mod 6 = 1: a(n) = (2/15)*n^5 + (403/162)*n^4 + (532/81)*n^3 + (151/27)*n^2 + (1361/405)*n + (301/162).
Empirical for n mod 6 = 2: a(n) = (2/15)*n^5 + (403/162)*n^4 + (532/81)*n^3 + (17/3)*n^2 + (1036/405)*n + (49/81).
Empirical for n mod 6 = 3: a(n) = (2/15)*n^5 + (403/162)*n^4 + (532/81)*n^3 + (17/3)*n^2 + (169/45)*n + (5/2).
Empirical for n mod 6 = 4: a(n) = (2/15)*n^5 + (403/162)*n^4 + (532/81)*n^3 + (151/27)*n^2 + (956/405)*n + (29/81).
Empirical for n mod 6 = 5: a(n) = (2/15)*n^5 + (403/162)*n^4 + (532/81)*n^3 + (17/3)*n^2 + (1441/405)*n + (341/162).

A250649 Number of length 5+1 0..n arrays with the sum of the maximum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

28, 280, 1424, 4853, 12473, 28379, 56088, 103712, 175998, 289559, 445513, 675267, 974698, 1392138, 1913166, 2619191, 3465655, 4583225, 5895042, 7580998, 9518912, 11977473, 14741143, 18198445, 22042896, 26774380, 31970892, 38321697, 45196741

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

Row 5 of A250646

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

R. H. Hardin, Table of n, a(n) for n = 1..153

Empirical: a(n) = -3*a(n-1) -4*a(n-2) +11*a(n-4) +21*a(n-5) +18*a(n-6) -6*a(n-7) -39*a(n-8) -53*a(n-9) -30*a(n-10) +22*a(n-11) +64*a(n-12) +64*a(n-13) +22*a(n-14) -30*a(n-15) -53*a(n-16) -39*a(n-17) -6*a(n-18) +18*a(n-19) +21*a(n-20) +11*a(n-21) -4*a(n-23) -3*a(n-24) -a(n-25)
Empirical for n mod 12 = 0: a(n) = (389983/207360)*n^5 + (130579/13824)*n^4 + (3643/576)*n^3 + (791/288)*n^2 + (467/60)*n + 1
Empirical for n mod 12 = 1: a(n) = (389983/207360)*n^5 + (63179/6912)*n^4 + (45683/6912)*n^3 + (11065/2592)*n^2 + (61501/7680)*n - (13183/6912)
Empirical for n mod 12 = 2: a(n) = (389983/207360)*n^5 + (130579/13824)*n^4 + (3643/576)*n^3 + (9199/5184)*n^2 + (23569/4320)*n + (67/864)
Empirical for n mod 12 = 3: a(n) = (389983/207360)*n^5 + (63179/6912)*n^4 + (14545/2304)*n^3 + (2155/576)*n^2 + (62941/7680)*n - (537/256)
Empirical for n mod 12 = 4: a(n) = (389983/207360)*n^5 + (130579/13824)*n^4 + (11441/1728)*n^3 + (8527/2592)*n^2 + (467/60)*n + (41/27)
Empirical for n mod 12 = 5: a(n) = (389983/207360)*n^5 + (63179/6912)*n^4 + (14545/2304)*n^3 + (7097/2592)*n^2 + (394789/69120)*n - (21631/6912)
Empirical for n mod 12 = 6: a(n) = (389983/207360)*n^5 + (130579/13824)*n^4 + (3643/576)*n^3 + (1591/576)*n^2 + (3721/480)*n + (25/32)
Empirical for n mod 12 = 7: a(n) = (389983/207360)*n^5 + (63179/6912)*n^4 + (45683/6912)*n^3 + (22211/5184)*n^2 + (62941/7680)*n - (10915/6912)
Empirical for n mod 12 = 8: a(n) = (389983/207360)*n^5 + (130579/13824)*n^4 + (3643/576)*n^3 + (4559/2592)*n^2 + (2963/540)*n + (8/27)
Empirical for n mod 12 = 9: a(n) = (389983/207360)*n^5 + (63179/6912)*n^4 + (14545/2304)*n^3 + (1073/288)*n^2 + (61501/7680)*n - (621/256)
Empirical for n mod 12 = 10: a(n) = (389983/207360)*n^5 + (130579/13824)*n^4 + (11441/1728)*n^3 + (17135/5184)*n^2 + (3721/480)*n + (1123/864)
Empirical for n mod 12 = 11: a(n) = (389983/207360)*n^5 + (63179/6912)*n^4 + (14545/2304)*n^3 + (14275/5184)*n^2 + (407749/69120)*n - (19363/6912)

A250650 Number of length 6+1 0..n arrays with the sum of the maximum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

72, 1061, 7696, 34441, 120114, 332827, 812004, 1749359, 3497934, 6469165, 11395070, 19047473, 30746306, 47793245, 72401338, 106583429, 153809996, 217072541, 301491734, 411350415, 553983224, 735181841, 965180792, 1251735269

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

Row 6 of A250646

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

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

A250651 Number of length 7+1 0..n arrays with the sum of the maximum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

120, 2870, 28238, 163043, 677505, 2225195, 6290716, 15474251, 34620063, 71045837, 136895633, 249167782, 432945014, 721867127, 1163471851, 1819556318, 2767225673, 4114863787, 5983678292, 8546815362, 11983543443, 16566644515

Offset: 1

R. H. Hardin, Nov 26 2014

nonn

Row 7 of A250646

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

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

cp's OEIS Frontend

A250640 Number of length n+1 0..2 arrays with the sum of the maximum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

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A250641 Number of length n+1 0..3 arrays with the sum of the maximum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

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A250642 Number of length n+1 0..4 arrays with the sum of the maximum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

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A250643 Number of length n+1 0..5 arrays with the sum of the maximum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

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A250644 Number of length n+1 0..6 arrays with the sum of the maximum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

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A250647 Number of length 3+1 0..n arrays with the sum of the maximum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

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A250648 Number of length 4+1 0..n arrays with the sum of the maximum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

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A250649 Number of length 5+1 0..n arrays with the sum of the maximum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

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A250650 Number of length 6+1 0..n arrays with the sum of the maximum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

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A250651 Number of length 7+1 0..n arrays with the sum of the maximum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.

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