A250167 -id:A250167 - cp's OEIS frontend

A250162 Number of length n+1 0..3 arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero.

4, 20, 96, 436, 1880, 7836, 32032, 129572, 521256, 2091052, 8376368, 33529908, 134168632, 536772668, 2147287104, 8589541444, 34358952008, 137437380684, 549752668240, 2199016964180, 8796080439384, 35184346923100, 140737438023776

Offset: 1

R. H. Hardin, Nov 13 2014

nonn

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

R. H. Hardin, Table of n, a(n) for n = 1..59

Column 3 of A250167.

Empirical: a(n) = 8*a(n-1) - 21*a(n-2) + 22*a(n-3) - 8*a(n-4).
Conjectures from Colin Barker, Nov 12 2018: (Start)
G.f.: 4*x*(1 - 3*x + 5*x^2) / ((1 - x)^2*(1 - 2*x)*(1 - 4*x)).
a(n) = 2*(2 - 3*2^n + 4^n + 2*n).
(End)

A250163 Number of length n+1 0..4 arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

5, 33, 211, 1269, 7109, 37881, 195927, 996933, 5029417, 25262121, 126608171, 633821781, 3171197325, 15861685497, 79324281727, 396666275397, 1983460173617, 9917674841193, 49589469690579, 247950578857365, 1239762467069077

Offset: 1

R. H. Hardin, Nov 13 2014

nonn

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

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

Column 4 of A250167.

Empirical: a(n) = 16*a(n-1) -105*a(n-2) +372*a(n-3) -783*a(n-4) +1008*a(n-5) -779*a(n-6) +332*a(n-7) -60*a(n-8).

Empirical g.f.: x*(5 - 47*x + 208*x^2 - 502*x^3 + 599*x^4 - 311*x^5 + 52*x^6 + 44*x^7) / ((1 - x)^4*(1 - 2*x)^2*(1 - 3*x)*(1 - 5*x)). - Colin Barker, Nov 12 2018

A250164 Number of length n+1 0..5 arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

6, 48, 380, 2860, 19896, 129648, 810964, 4962056, 30034672, 180893724, 1087112084, 6527090276, 39173693352, 235070531992, 1410496377492, 8463170413616, 50779536937024, 304678626418660, 1828075665965204, 10968465043204908

Offset: 1

R. H. Hardin, Nov 13 2014

nonn

Column 5 of A250167

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

R. H. Hardin, Table of n, a(n) for n = 1..27

A250165 Number of length n+1 0..6 arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

7, 67, 639, 5831, 49037, 380939, 2810751, 20169871, 142786013, 1004527983, 7047533399, 49383700439, 345855478109, 2421574390899, 16953120700735, 118679602696751, 830786561364589, 5815618832245175, 40709771502502967

Offset: 1

R. H. Hardin, Nov 13 2014

nonn

Column 6 of A250167

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

R. H. Hardin, Table of n, a(n) for n = 1..29

A250166 Number of length n+1 0..7 arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

8, 88, 976, 10460, 103556, 938128, 7989940, 65768448, 532548628, 4281269376, 34316191340, 274736779444, 2198552029712, 17590557578440, 140731669092632, 1125878500233800, 9007118671839640, 72057285402401144, 576459555378977560

Offset: 1

R. H. Hardin, Nov 13 2014

nonn

Column 7 of A250167

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

R. H. Hardin, Table of n, a(n) for n = 1..22

A250168 Number of length 3+1 0..n arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

8, 37, 96, 211, 380, 639, 976, 1437, 2000, 2721, 3568, 4607, 5796, 7211, 8800, 10649, 12696, 15037, 17600, 20491, 23628, 27127, 30896, 35061, 39520, 44409, 49616, 55287, 61300, 67811, 74688, 82097, 89896, 98261, 107040, 116419, 126236, 136687, 147600

Offset: 1

R. H. Hardin, Nov 13 2014

nonn

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

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

Row 3 of A250167.

Empirical: a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6).
Empirical for n mod 2 = 0: a(n) = (29/12)*n^3 + (11/4)*n^2 + (17/6)*n + 1.
Empirical for n mod 2 = 1: a(n) = (29/12)*n^3 + (11/4)*n^2 + (19/12)*n + (5/4).
Empirical g.f.: x*(8 + 21*x + 14*x^2 + 14*x^3 + 2*x^4 - x^5) / ((1 - x)^4*(1 + x)^2). - Colin Barker, Nov 12 2018

A250169 Number of length 4+1 0..n arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

16, 119, 436, 1269, 2860, 5831, 10460, 17765, 27984, 42611, 61752, 87477, 119672, 161051, 211212, 273601, 347428, 436963, 540948, 664553, 805976, 971367, 1158288, 1373969, 1615248, 1890503, 2195780, 2540693, 2920396, 3345831, 3811180, 4328789

Offset: 1

R. H. Hardin, Nov 13 2014

nonn

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

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

Row 4 of A250167.

Empirical: a(n) = a(n-1) + 2*a(n-2) - a(n-3) - a(n-4) - 2*a(n-5) + 2*a(n-7) + a(n-8) + a(n-9) - 2*a(n-10) - a(n-11) + a(n-12).
Empirical for n mod 12 = 0: a(n) = (197/48)*n^4 + (5/12)*n^3 + (45/4)*n^2 + (8/3)*n + 1
Empirical for n mod 12 = 1: a(n) = (197/48)*n^4 + (5/12)*n^3 + (69/8)*n^2 + (77/12)*n - (57/16)
Empirical for n mod 12 = 2: a(n) = (197/48)*n^4 + (5/12)*n^3 + (45/4)*n^2 + (8/3)*n - (1/3)
Empirical for n mod 12 = 3: a(n) = (197/48)*n^4 + (5/12)*n^3 + (69/8)*n^2 + (77/12)*n - (73/16)
Empirical for n mod 12 = 4: a(n) = (197/48)*n^4 + (5/12)*n^3 + (45/4)*n^2 + (8/3)*n + 1
Empirical for n mod 12 = 5: a(n) = (197/48)*n^4 + (5/12)*n^3 + (69/8)*n^2 + (77/12)*n - (235/48)
Empirical for n mod 12 = 6: a(n) = (197/48)*n^4 + (5/12)*n^3 + (45/4)*n^2 + (8/3)*n + 1
Empirical for n mod 12 = 7: a(n) = (197/48)*n^4 + (5/12)*n^3 + (69/8)*n^2 + (77/12)*n - (73/16)
Empirical for n mod 12 = 8: a(n) = (197/48)*n^4 + (5/12)*n^3 + (45/4)*n^2 + (8/3)*n - (1/3)
Empirical for n mod 12 = 9: a(n) = (197/48)*n^4 + (5/12)*n^3 + (69/8)*n^2 + (77/12)*n - (57/16)
Empirical for n mod 12 = 10: a(n) = (197/48)*n^4 + (5/12)*n^3 + (45/4)*n^2 + (8/3)*n + 1
Empirical for n mod 12 = 11: a(n) = (197/48)*n^4 + (5/12)*n^3 + (69/8)*n^2 + (77/12)*n - (283/48).
Empirical g.f.: x*(16 + 103*x + 285*x^2 + 611*x^3 + 854*x^4 + 1020*x^5 + 852*x^6 + 612*x^7 + 274*x^8 + 101*x^9 - x^10 + x^11) / ((1 - x)^5*(1 + x)^3*(1 + x^2)*(1 + x + x^2)). - Colin Barker, Nov 12 2018

A250170 Number of length 5+1 0..n arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

32, 373, 1880, 7109, 19896, 49037, 103556, 203615, 364900, 624811, 1006084, 1570791, 2347840, 3431579, 4856212, 6757417, 9171308, 12285541, 16134624, 20968689, 26816804, 34003157, 42544984, 52855367, 64932468, 79290519, 95903144

Offset: 1

R. H. Hardin, Nov 13 2014

nonn

Row 5 of A250167

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

R. H. Hardin, Table of n, a(n) for n = 1..66

Empirical: a(n) = a(n-2) +a(n-3) +2*a(n-4) -a(n-6) -3*a(n-7) -3*a(n-8) -a(n-9) +3*a(n-11) +4*a(n-12) +3*a(n-13) -a(n-15) -3*a(n-16) -3*a(n-17) -a(n-18) +2*a(n-20) +a(n-21) +a(n-22) -a(n-24)
Empirical: also a polynomial of degree 5 plus a cubic quasipolynomial with period 60, the first 12 being:
Empirical for n mod 60 = 0: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (19639/216)*n^3 - (82547/720)*n^2 + (299/4)*n + 1
Empirical for n mod 60 = 1: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (74029/864)*n^3 - (133189/1440)*n^2 - (223/64)*n + (457247/8640)
Empirical for n mod 60 = 2: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (19639/216)*n^3 - (82547/720)*n^2 + (2339/36)*n + (7721/270)
Empirical for n mod 60 = 3: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (74029/864)*n^3 - (133189/1440)*n^2 - (703/64)*n + (7753/64)
Empirical for n mod 60 = 4: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (19639/216)*n^3 - (82547/720)*n^2 + (299/4)*n - (1141/135)
Empirical for n mod 60 = 5: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (74029/864)*n^3 - (133189/1440)*n^2 - (7639/576)*n + (217043/1728)
Empirical for n mod 60 = 6: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (19639/216)*n^3 - (82547/720)*n^2 + (299/4)*n - (157/10)
Empirical for n mod 60 = 7: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (74029/864)*n^3 - (133189/1440)*n^2 - (703/64)*n + (893567/8640)
Empirical for n mod 60 = 8: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (19639/216)*n^3 - (82547/720)*n^2 + (2339/36)*n + (1223/27)
Empirical for n mod 60 = 9: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (74029/864)*n^3 - (133189/1440)*n^2 - (223/64)*n + (24653/320)
Empirical for n mod 60 = 10: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (19639/216)*n^3 - (82547/720)*n^2 + (299/4)*n - (1531/54)
Empirical for n mod 60 = 11: a(n) = (6943/960)*n^5 - (1143/64)*n^4 + (74029/864)*n^3 - (133189/1440)*n^2 - (11959/576)*n + (1493887/8640)

A250171 Number of length 6+1 0..n arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

64, 1151, 7836, 37881, 129648, 380939, 938128, 2121089, 4309040, 8284391, 14826764, 25544585, 41805464, 66528651, 101887084, 152748637, 222278752, 318099483, 444552268, 612989717, 829094428, 1109083919, 1460065140

Offset: 1

R. H. Hardin, Nov 13 2014

nonn

Row 6 of A250167

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

R. H. Hardin, Table of n, a(n) for n = 1..32

A250172 Number of length 7+1 0..n arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero.

Original entry on oeis.org

128, 3517, 32032, 195927, 810964, 2810751, 7989940, 20567199, 46931176, 100480363, 198506588, 375153177, 669200436, 1155420975, 1910171088, 3080038929, 4801129076, 7337318733, 10913397192, 15974820909, 22870564032

Offset: 1

R. H. Hardin, Nov 13 2014

nonn

Row 7 of A250167

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

R. H. Hardin, Table of n, a(n) for n = 1..24

cp's OEIS Frontend

A250162 Number of length n+1 0..3 arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero.

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A250163 Number of length n+1 0..4 arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero.

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A250164 Number of length n+1 0..5 arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero.

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A250165 Number of length n+1 0..6 arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero.

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A250166 Number of length n+1 0..7 arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero.

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A250168 Number of length 3+1 0..n arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero.

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A250169 Number of length 4+1 0..n arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero.

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A250170 Number of length 5+1 0..n arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero.

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A250171 Number of length 6+1 0..n arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero.

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A250172 Number of length 7+1 0..n arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero.

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