A242322 -id:A242322 - cp's OEIS frontend

A242317 Number of length n+2+2 0..2 arrays with every value 0..2 appearing at least once in every consecutive 2+3 elements, and new values 0..2 introduced in order.

25, 61, 145, 337, 781, 1829, 4269, 9957, 23233, 54225, 126533, 295265, 689021, 1607877, 3752057, 8755625, 20431737, 47678569, 111260509, 259632437, 605866385, 1413822053, 3299230409, 7698933081, 17965877829, 41924350093, 97832744293

Offset: 1

R. H. Hardin, May 10 2014

nonn

Column 2 of A242322.

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

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

Cf. A242322.

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

Empirical g.f.: x*(25 + 36*x + 34*x^2 + 20*x^3 - 18*x^4 - 13*x^5) / ((1 + x)*(1 - 2*x - 2*x^3 + x^5)). - Colin Barker, Mar 19 2018

A242318 Number of length n+3+2 0..3 arrays with every value 0..3 appearing at least once in every consecutive 3+3 elements, and new values 0..3 introduced in order.

Original entry on oeis.org

65, 185, 503, 1316, 3398, 8801, 23069, 60197, 156887, 408962, 1066514, 2781611, 7253453, 18914369, 49323167, 128621684, 335409314, 874649537, 2280834353, 5947765493, 15510073823, 40445831522, 105471145814, 275038567523

Offset: 1

R. H. Hardin, May 10 2014

nonn

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

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

Column 3 of A242322.

Empirical: a(n) = a(n-1) + 2*a(n-2) + 3*a(n-3) + 5*a(n-4) + 6*a(n-5) - a(n-6) - a(n-7) - a(n-9) - a(n-10).

Empirical g.f.: x*(65 + 120*x + 188*x^2 + 248*x^3 + 196*x^4 - 53*x^5 - 36*x^6 - 16*x^7 - 49*x^8 - 35*x^9) / (1 - x - 2*x^2 - 3*x^3 - 5*x^4 - 6*x^5 + x^6 + x^7 + x^9 + x^10). - Colin Barker, Nov 01 2018

A242319 Number of length n+4+2 0..4 arrays with every value 0..4 appearing at least once in every consecutive 4+3 elements, and new values 0..4 introduced in order.

Original entry on oeis.org

140, 440, 1300, 3648, 10012, 27368, 75236, 208976, 577964, 1596216, 4408020, 12176768, 33645500, 92967176, 256849892, 709617776, 1960543660, 5416680632, 14965468916, 41347189280, 114235439996, 315613828040, 871989852740

Offset: 1

R. H. Hardin, May 10 2014

nonn

Column 4 of A242322

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

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

Empirical: a(n) = a(n-1) +2*a(n-2) +4*a(n-3) +6*a(n-4) +10*a(n-5) +12*a(n-6) -4*a(n-7) -6*a(n-8) -6*a(n-9) -2*a(n-11) -2*a(n-12) +a(n-14) +a(n-15)

A242320 Number of length n+5+2 0..5 arrays with every value 0..5 appearing at least once in every consecutive 5+3 elements, and new values 0..5 introduced in order.

Original entry on oeis.org

266, 896, 2801, 8231, 23486, 66366, 187671, 533801, 1530356, 4371836, 12472691, 35574971, 101483076, 289556006, 826266561, 2357781941, 6727551746, 19195784876, 54771887681, 156283330211, 445932182766, 1272403116946

Offset: 1

R. H. Hardin, May 10 2014

nonn

Column 5 of A242322.

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

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

Cf. A242322.

Empirical: a(n) = a(n-1) +2*a(n-2) +4*a(n-3) +7*a(n-4) +13*a(n-5) +22*a(n-6) +28*a(n-7) -4*a(n-8) -6*a(n-9) -6*a(n-10) -4*a(n-12) -10*a(n-13) -10*a(n-14) +a(n-16) +a(n-17) +a(n-20) +a(n-21).

A242321 Number of length n+6+2 0..6 arrays with every value 0..6 appearing at least once in every consecutive 6+3 elements, and new values 0..6 introduced in order.

Original entry on oeis.org

462, 1638, 5334, 16194, 47466, 137166, 395166, 1141290, 3312546, 9669270, 28147842, 81849030, 237928206, 691657866, 2010909066, 5847101166, 17002342422, 49439204898, 143753422386, 417985825410, 1215362762970, 3533881164654

Offset: 1

R. H. Hardin, May 10 2014

nonn

Column 6 of A242322

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

R. H. Hardin, Table of n, a(n) for n = 1..63

Empirical: a(n) = a(n-1) +2*a(n-2) +4*a(n-3) +8*a(n-4) +14*a(n-5) +26*a(n-6) +44*a(n-7) +56*a(n-8) -11*a(n-9) -19*a(n-10) -28*a(n-11) -28*a(n-12) -8*a(n-14) -20*a(n-15) -20*a(n-16) +5*a(n-18) +11*a(n-19) +10*a(n-20) +2*a(n-23) +2*a(n-24) -a(n-27) -a(n-28)

cp's OEIS Frontend

A242317 Number of length n+2+2 0..2 arrays with every value 0..2 appearing at least once in every consecutive 2+3 elements, and new values 0..2 introduced in order.

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A242318 Number of length n+3+2 0..3 arrays with every value 0..3 appearing at least once in every consecutive 3+3 elements, and new values 0..3 introduced in order.

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A242319 Number of length n+4+2 0..4 arrays with every value 0..4 appearing at least once in every consecutive 4+3 elements, and new values 0..4 introduced in order.

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A242320 Number of length n+5+2 0..5 arrays with every value 0..5 appearing at least once in every consecutive 5+3 elements, and new values 0..5 introduced in order.

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A242321 Number of length n+6+2 0..6 arrays with every value 0..6 appearing at least once in every consecutive 6+3 elements, and new values 0..6 introduced in order.

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