A245950 -id:A245950 - cp's OEIS frontend

A245945 Number of length n+3 0..2 arrays with some pair in every consecutive four terms totalling exactly 2.

71, 197, 545, 1501, 4145, 11441, 31577, 87161, 240581, 664051, 1832917, 5059221, 13964475, 38544783, 106391413, 293661867, 810566283, 2237327253, 6175476757, 17045567707, 47049222251, 129865390965, 358454804639, 989407924729

Offset: 1

R. H. Hardin, Aug 08 2014

nonn

			Some solutions for n=8:
..0....1....1....1....2....1....0....0....1....1....2....1....0....0....1....2
..1....1....2....1....0....2....2....1....0....2....0....0....0....1....1....0
..2....2....0....2....1....0....2....0....2....2....0....1....2....1....0....0
..0....1....0....0....1....1....0....2....0....1....2....2....0....0....1....1
..1....2....1....1....1....0....2....1....0....0....2....1....1....2....1....2
..0....1....1....0....1....1....2....0....1....1....0....0....0....2....1....1
..2....2....1....2....2....1....1....0....1....2....2....1....1....1....2....0
..2....0....1....2....1....0....0....1....0....2....0....0....2....0....1....2
..0....1....0....0....2....0....1....1....0....0....2....2....0....2....2....0
..0....1....1....1....0....2....1....2....2....2....2....1....2....0....1....0
..2....2....1....1....0....2....2....1....2....1....1....0....0....0....2....2

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

Column 2 of A245950.

Empirical: a(n) = 2*a(n-1) + 2*a(n-2) + a(n-3) - a(n-4) - 2*a(n-5) - 2*a(n-6) - a(n-7) + a(n-8) + a(n-9).

Empirical g.f.: x*(71 + 55*x + 9*x^2 - 54*x^3 - 73*x^4 - 57*x^5 - 15*x^6 + 36*x^7 + 27*x^8) / ((1 - x)*(1 - x - 3*x^2 - 4*x^3 - 3*x^4 - x^5 + x^6 + 2*x^7 + x^8)). - Colin Barker, Nov 05 2018

A245946 Number of length n+3 0..4 arrays with some pair in every consecutive four terms totalling exactly 4.

Original entry on oeis.org

453, 1889, 7769, 31465, 128649, 525041, 2141609, 8740385, 35666177, 145538749, 593901081, 2423511809, 9889552885, 40356071813, 164679993617, 672005573917, 2742236755101, 11190178304945, 45663487141625, 186337877072653

Offset: 1

R. H. Hardin, Aug 08 2014

nonn

Column 4 of A245950.

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

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

Cf. A245950.

Empirical: a(n) = 3*a(n-1) +5*a(n-2) +3*a(n-3) -10*a(n-4) -37*a(n-5) -48*a(n-6) -37*a(n-7) +83*a(n-8) +143*a(n-9) +5*a(n-10) -11*a(n-11) -41*a(n-12) -10*a(n-13) -2*a(n-14) +3*a(n-15).

A245947 Number of length n+3 0..5 arrays with some pair in every consecutive four terms totalling exactly 5.

Original entry on oeis.org

834, 3966, 18384, 82968, 381222, 1744494, 7972932, 36489120, 166920402, 763564758, 3493201536, 15980209872, 73104350502, 334430964150, 1529917916484, 6998905422984, 32017855579074, 146471872453902, 670063969035792

Offset: 1

R. H. Hardin, Aug 08 2014

nonn

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

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

Column 5 of A245950.

Empirical: a(n) = 3*a(n-1) + 5*a(n-2) + 13*a(n-3) - 13*a(n-4) - a(n-5) - 3*a(n-6) + a(n-7).

Empirical g.f.: 6*x*(139 + 244*x + 386*x^2 - 476*x^3 - 53*x^4 - 102*x^5 + 36*x^6) / (1 - 3*x - 5*x^2 - 13*x^3 + 13*x^4 + x^5 + 3*x^6 - x^7). - Colin Barker, Nov 05 2018

A245948 Number of length n+3 0..6 arrays with some pair in every consecutive four terms totalling exactly 6.

Original entry on oeis.org

1435, 7669, 39721, 199141, 1021225, 5208673, 26526337, 135336793, 690045061, 3518298991, 17940920173, 91480646389, 466463146399, 2378531818147, 12128251046821, 61842638080231, 315339231002215, 1607932492222021

Offset: 1

R. H. Hardin, Aug 08 2014

nonn

Column 6 of A245950.

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

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

Cf. A245950.

Empirical: a(n) = 4*a(n-1) +8*a(n-2) +2*a(n-3) -39*a(n-4) -139*a(n-5) -175*a(n-6) -179*a(n-7) +980*a(n-8) +1638*a(n-9) -1266*a(n-10) -210*a(n-11) -352*a(n-12) +123*a(n-13) +24*a(n-14) +19*a(n-15) -5*a(n-16).

A245949 Number of length n+3 0..7 arrays with some pair in every consecutive four terms totalling exactly 7.

Original entry on oeis.org

2216, 13064, 73728, 397504, 2217096, 12257032, 67596992, 373997376, 2066660136, 11420014856, 63122102528, 348845096320, 1927940409608, 10655229621512, 58887811241024, 325454196462720, 1798683415254952, 9940745874984456

Offset: 1

R. H. Hardin, Aug 08 2014

nonn

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

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

Column 7 of A245950.

Empirical: a(n) = 3*a(n-1) + 9*a(n-2) + 31*a(n-3) - 19*a(n-4) - 3*a(n-5) - 5*a(n-6) + a(n-7).

Empirical g.f.: 8*x*(277 + 802*x + 1824*x^2 - 1244*x^3 - 231*x^4 - 312*x^5 + 64*x^6) / (1 - 3*x - 9*x^2 - 31*x^3 + 19*x^4 + 3*x^5 + 5*x^6 - x^7). - Colin Barker, Nov 05 2018

A245951 Number of length 1+3 0..n arrays with some pair in every consecutive four terms totalling exactly n.

Original entry on oeis.org

14, 71, 196, 453, 834, 1435, 2216, 3305, 4630, 6351, 8364, 10861, 13706, 17123, 20944, 25425, 30366, 36055, 42260, 49301, 56914, 65451, 74616, 84793, 95654, 107615, 120316, 134205, 148890, 164851, 181664, 199841, 218926, 239463, 260964, 284005

Offset: 1

R. H. Hardin, Aug 08 2014

nonn

			Some solutions for n=10:
..6....5....7...10....6....7....6....0....3....6....1....8....5....1...10....8
..5....7....5....1...10...10....9...10....7....5...10...10....5....5....9....2
..3....6...10....9....4....6....6....8....7....4....9....4....2....5....7....1
..7....4....5....7...10....4....1...10....7....6....5....0....0....2....0....6

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

Row 1 of A245950.

Empirical: a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6).
Conjectures from Colin Barker, Nov 05 2018: (Start)
G.f.: x*(14 + 43*x + 40*x^2 + 46*x^3 + 2*x^4 - x^5) / ((1 - x)^4*(1 + x)^2).
a(n) = 1 + 5*n + 3*n^2 + 6*n^3 for n even.
a(n) = 4 + n + 3*n^2 + 6*n^3 for n odd.
(End)

A245952 Number of length 2+3 0..n arrays with some pair in every consecutive four terms totalling exactly n.

Original entry on oeis.org

26, 197, 676, 1889, 3966, 7669, 13064, 21281, 32290, 47621, 67116, 92737, 124166, 163829, 211216, 269249, 337194, 418501, 512180, 622241, 747406, 892277, 1055256, 1241569, 1449266, 1684229, 1944124, 2235521, 2555670, 2911861, 3300896, 3730817

Offset: 1

R. H. Hardin, Aug 08 2014

nonn

			Some solutions for n=10:
..3....1....2....0....6....0....7....8....4...10....2....9....9....3....0....3
..9....1....2....3....6....8....0....5....9....5....6....3....2....0....1....2
..1....9...10...10....2....2...10....5....1....6....1....7....0...10....9....8
..1....6....0....0....4....0....9....0....6....5....4....2....8....6....8...10
..1....8...10....2...10....9....6....6....1....5....7....4....1....3...10....2

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

Row 2 of A245950.

Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - 6*a(n-3) + 6*a(n-5) - 2*a(n-6) - 2*a(n-7) + a(n-8).
Conjectures from Colin Barker, Nov 05 2018: (Start)
G.f.: x*(26 + 145*x + 230*x^2 + 299*x^3 + 18*x^4 - 141*x^5 - 2*x^6 + x^7) / ((1 - x)^5*(1 + x)^3).
a(n) = 1 + 12*n - 5*n^2 + 18*n^3 + 3*n^4 for n even.
a(n) = 16 - 5*n - 6*n^2 + 18*n^3 + 3*n^4 for n odd.
(End)

A245953 Number of length 3+3 0..n arrays with some pair in every consecutive four terms totalling exactly n.

Original entry on oeis.org

48, 545, 2304, 7769, 18384, 39721, 73728, 130193, 211440, 332561, 496128, 723625, 1017744, 1407449, 1895424, 2519201, 3281328, 4228993, 5364480, 6745721, 8374608, 10320905, 12585984, 15252529, 18321264, 21888881, 25955328, 30632393, 35919120

Offset: 1

R. H. Hardin, Aug 08 2014

nonn

			Some solutions for n=8:
..3....4....6....3....2....2....5....0....0....3....1....3....2....6....5....1
..1....3....7....8....8....0....1....1....6....2....8....8....6....3....4....5
..2....4....2....5....7....8....5....4....8....4....0....4....1....6....2....3
..6....5....8....3....1....4....7....7....3....5....6....5....5....5....6....8
..3....1....6....1....8....6....1....6....5....4....6....4....2....2....6....0
..2....7....2....2....1....0....4....2....2....1....2....8....6....1....0....8

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

Row 3 of A245950.

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).
Conjectures from Colin Barker, Nov 05 2018: (Start)
G.f.: x*(48 + 401*x + 669*x^2 + 1241*x^3 - 851*x^4 - 557*x^5 + 7*x^6 + 3*x^7 - x^8) / ((1 - x)^6*(1 + x)^3).
a(n) = 1 + 26*n - 17*n^2 + 24*n^3 + 21*n^4 + n^5 for n even.
a(n) = 39 - n - 36*n^2 + 24*n^3 + 21*n^4 + n^5 for n odd.
(End)

A245954 Number of length 4+3 0..n arrays with some pair in every consecutive four terms totalling exactly n.

Original entry on oeis.org

88, 1501, 7744, 31465, 82968, 199141, 397504, 754321, 1292440, 2144941, 3335808, 5074681, 7380184, 10560565, 14620288, 19990561, 26650584, 35181181, 45522880, 58435081, 73803928, 92598661, 114633024, 141119665, 171779608, 208104781

Offset: 1

R. H. Hardin, Aug 08 2014

nonn

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

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

Row 4 of A245950

Empirical: a(n) = 2*a(n-1) + 3*a(n-2) - 8*a(n-3) - 2*a(n-4) + 12*a(n-5) - 2*a(n-6) - 8*a(n-7) + 3*a(n-8) + 2*a(n-9) - a(n-10).
Conjectures from Colin Barker, Nov 05 2018: (Start)
G.f.: x*(88 + 1325*x + 4478*x^2 + 12178*x^3 + 8990*x^4 + 2708*x^5 - 310*x^6 - 658*x^7 + 2*x^8 - x^9) / ((1 - x)^6*(1 + x)^4).
a(n) = 1 + 34*n + 6*n^2 - 16*n^3 + 66*n^4 + 15*n^5 for n even.
a(n) = 58 + 57*n - 80*n^2 - 28*n^3 + 66*n^4 + 15*n^5 for n odd.
(End)

A245955 Number of length 5+3 0..n arrays with some pair in every consecutive four terms totalling exactly n.

Original entry on oeis.org

162, 4145, 26244, 128649, 381222, 1021225, 2217096, 4555697, 8345130, 14757441, 24276492, 38959225, 59493294, 89187449, 128950032, 183778785, 254805426, 349227217, 468384660, 622261481, 812372022, 1052152905, 1343233944

Offset: 1

R. H. Hardin, Aug 08 2014

nonn

Row 5 of A245950

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

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

Empirical: a(n) = 2*a(n-1) +4*a(n-2) -10*a(n-3) -5*a(n-4) +20*a(n-5) -20*a(n-7) +5*a(n-8) +10*a(n-9) -4*a(n-10) -2*a(n-11) +a(n-12)

cp's OEIS Frontend

A245945 Number of length n+3 0..2 arrays with some pair in every consecutive four terms totalling exactly 2.

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A245946 Number of length n+3 0..4 arrays with some pair in every consecutive four terms totalling exactly 4.

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A245947 Number of length n+3 0..5 arrays with some pair in every consecutive four terms totalling exactly 5.

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A245948 Number of length n+3 0..6 arrays with some pair in every consecutive four terms totalling exactly 6.

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A245949 Number of length n+3 0..7 arrays with some pair in every consecutive four terms totalling exactly 7.

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A245951 Number of length 1+3 0..n arrays with some pair in every consecutive four terms totalling exactly n.

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A245952 Number of length 2+3 0..n arrays with some pair in every consecutive four terms totalling exactly n.

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A245953 Number of length 3+3 0..n arrays with some pair in every consecutive four terms totalling exactly n.

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A245954 Number of length 4+3 0..n arrays with some pair in every consecutive four terms totalling exactly n.

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A245955 Number of length 5+3 0..n arrays with some pair in every consecutive four terms totalling exactly n.

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