A268327 -id:A268327 - cp's OEIS frontend

A268320 Number of length-(n+1) 0..n arrays with new values introduced in sequential order, and with new repeated values introduced in sequential order, both starting with zero.

2, 4, 11, 33, 114, 435, 1829, 8377, 41504, 220958, 1256927, 7602273, 48676925, 328685063, 2332565079, 17344752142, 134774766541, 1091701884974, 9198355199792, 80459135884925, 729337831748484, 6840215461149149

Offset: 1

R. H. Hardin, Feb 01 2016

nonn

Diagonal of A268327.

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

R. H. Hardin, Table of n, a(n) for n = 1..147

Cf. A268327.

A268321 Number of length-(n+1) 0..2 arrays with new values introduced in sequential order, and with new repeated values introduced in sequential order, both starting with zero.

Original entry on oeis.org

2, 4, 10, 25, 66, 177, 485, 1348, 3797, 10812, 31076, 90015, 262432, 769199, 2264475, 6690450, 19825011, 58884842, 175238730, 522316253, 1558776782, 4656673837, 13922711281, 41654206400, 124688153137, 373402997944, 1118614401040

Offset: 1

R. H. Hardin, Feb 01 2016

nonn

			Some solutions for n=10:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....1....0....0....1....0....1....0....0....0....0....0....1....1....1
..1....0....0....1....0....0....1....2....1....1....1....1....1....0....0....2
..2....0....2....1....1....2....1....0....2....1....1....0....2....2....1....1
..1....0....0....2....1....0....1....0....1....0....0....1....0....0....2....0
..2....1....0....1....1....1....1....0....1....2....1....1....2....0....0....1
..1....1....2....1....1....2....1....1....2....2....0....1....1....2....1....0
..1....0....0....0....1....0....0....2....0....0....0....2....2....1....2....0
..2....1....0....2....2....2....0....0....0....2....1....2....0....1....1....0
..1....2....2....1....0....0....2....1....1....0....2....1....0....2....2....2
..1....1....1....1....0....2....2....0....1....1....0....2....1....0....1....0

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

Column 2 of A268327.

Empirical: a(n) = 7*a(n-1) - 14*a(n-2) + 21*a(n-4) - 7*a(n-5) - 6*a(n-6).

Empirical g.f.: x*(2 - 10*x + 10*x^2 + 11*x^3 - 11*x^4 - 5*x^5) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - 3*x)*(1 - 2*x - x^2)). - Colin Barker, Jan 13 2019

A268322 Number of length-(n+1) 0..3 arrays with new values introduced in sequential order, and with new repeated values introduced in sequential order, both starting with zero.

Original entry on oeis.org

2, 4, 11, 32, 102, 337, 1148, 3984, 14030, 49973, 179735, 652010, 2383857, 8779485, 32555471, 121497802, 456178652, 1722502343, 6538543106, 24942393310, 95581407132, 367817900179, 1420912978925, 5508514801624, 21423891255215

Offset: 1

R. H. Hardin, Feb 01 2016

nonn

Column 3 of A268327.

			Some solutions for n=10
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....0....0....1....1....1....1....1....0....1....1....1....0....0....0
..2....0....0....0....0....2....2....2....0....1....2....2....2....1....0....1
..1....1....1....0....2....3....1....1....0....2....1....0....1....2....1....1
..3....2....2....1....1....2....0....0....0....3....3....0....2....0....1....1
..2....1....0....0....2....0....3....2....1....1....0....2....0....2....2....1
..3....2....3....2....0....1....2....3....0....0....0....1....1....3....0....1
..0....3....0....3....2....0....0....0....1....1....1....2....0....2....1....2
..0....0....0....1....1....3....1....1....1....2....1....0....1....1....1....3
..0....0....0....3....2....0....3....2....0....0....0....3....0....2....0....0
..1....1....0....2....0....0....2....1....2....0....3....1....1....0....0....0

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

Cf. A268327.

Empirical: a(n) = 15*a(n-1) -83*a(n-2) +181*a(n-3) +20*a(n-4) -632*a(n-5) +445*a(n-6) +849*a(n-7) -637*a(n-8) -673*a(n-9) +208*a(n-10) +260*a(n-11) +48*a(n-12)

A268323 Number of length-(n+1) 0..4 arrays with new values introduced in sequential order, and with new repeated values introduced in sequential order, both starting with zero.

Original entry on oeis.org

2, 4, 11, 33, 113, 418, 1644, 6729, 28306, 121290, 526528, 2307684, 10189912, 45272176, 202209217, 907511800, 4091094290, 18521091171, 84191453893, 384234672892, 1760416403153, 8096423923987, 37376700482989, 173184754445281

Offset: 1

R. H. Hardin, Feb 01 2016

nonn

Column 4 of A268327.

			Some solutions for n=10
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....0....1....1....1....1....0....1....0....0....1....0....1....1
..2....0....2....1....2....0....0....0....0....0....0....1....0....0....2....2
..0....2....0....0....1....2....0....0....1....2....1....2....1....1....0....0
..1....3....0....1....3....3....2....2....2....3....1....3....2....1....1....0
..0....2....3....2....2....2....3....1....1....4....1....1....0....2....0....0
..3....4....0....0....3....4....0....3....2....2....2....2....1....2....3....3
..4....0....3....2....2....0....0....1....3....0....1....1....2....3....1....1
..0....2....0....1....1....1....0....0....4....3....1....0....3....4....0....4
..1....1....0....1....4....4....4....0....0....1....2....1....4....3....4....0
..4....0....4....0....3....3....2....4....4....0....0....2....3....4....0....3

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

Cf. A268327.

Empirical: a(n) = 30*a(n-1) -383*a(n-2) +2665*a(n-3) -10530*a(n-4) +20413*a(n-5) +1810*a(n-6) -87142*a(n-7) +111699*a(n-8) +116304*a(n-9) -292159*a(n-10) -83751*a(n-11) +371556*a(n-12) +93673*a(n-13) -257980*a(n-14) -122812*a(n-15) +60076*a(n-16) +59180*a(n-17) +15912*a(n-18) +1440*a(n-19)

A268324 Number of length-(n+1) 0..5 arrays with new values introduced in sequential order, and with new repeated values introduced in sequential order, both starting with zero.

Original entry on oeis.org

2, 4, 11, 33, 114, 434, 1806, 8052, 37851, 184910, 928406, 4752055, 24656385, 129183323, 681695654, 3616896810, 19273025959, 103063766844, 552827229141, 2973435835535, 16033214329525, 86659280236610, 469464972714177

Offset: 1

R. H. Hardin, Feb 01 2016

nonn

Column 5 of A268327.

			Some solutions for n=10
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....1....0....0....0....0....0....0....1....0....0....0....0
..1....0....0....1....0....1....1....1....0....1....1....2....1....1....1....1
..1....1....0....2....1....2....2....2....1....1....2....0....2....1....2....2
..2....1....1....1....0....1....0....1....2....2....1....0....0....1....3....1
..3....1....2....1....0....2....3....0....0....2....3....3....1....1....4....3
..2....2....3....2....2....3....2....1....2....2....4....1....0....0....3....2
..3....3....0....1....0....4....1....1....1....2....3....2....1....1....0....4
..0....2....1....3....1....1....2....3....3....3....5....4....1....2....4....3
..2....4....3....2....2....3....4....4....1....3....0....5....0....2....1....0
..3....1....2....0....1....1....0....5....3....3....2....2....0....3....4....3

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

Cf. A268327.

Empirical: a(n) = 52*a(n-1) -1217*a(n-2) +16835*a(n-3) -151495*a(n-4) +913335*a(n-5) -3595675*a(n-6) +7981675*a(n-7) -1977562*a(n-8) -42002621*a(n-9) +99434620*a(n-10) +11892832*a(n-11) -369952047*a(n-12) +312076090*a(n-13) +749849987*a(n-14) -1016956079*a(n-15) -1168160519*a(n-16) +1710725071*a(n-17) +1710086539*a(n-18) -1618310265*a(n-19) -2126314760*a(n-20) +451613225*a(n-21) +1594319858*a(n-22) +601430554*a(n-23) -317807648*a(n-24) -383121792*a(n-25) -161486112*a(n-26) -36051552*a(n-27) -4243968*a(n-28) -207360*a(n-29)

A268325 Number of length-(n+1) 0..6 arrays with new values introduced in sequential order, and with new repeated values introduced in sequential order, both starting with zero.

Original entry on oeis.org

2, 4, 11, 33, 114, 435, 1828, 8347, 40967, 213476, 1167038, 6620563, 38616800, 229908144, 1389394409, 8488437842, 52275301038, 323844494931, 2015202856151, 12583558074610, 78792289312786, 494476637793884, 3109144620092506

Offset: 1

R. H. Hardin, Feb 01 2016

nonn

Column 6 of A268327.

			Some solutions for n=9
..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....1....0....1....0....1....0....1
..2....2....2....2....2....0....0....2....0....2....1....2....1....2....1....2
..0....3....3....3....3....2....0....3....0....0....2....3....0....3....1....1
..3....2....4....4....2....3....0....4....2....2....3....4....2....1....0....0
..4....4....2....0....0....4....2....0....0....3....4....3....3....2....1....3
..3....0....5....3....0....5....3....4....0....0....3....2....0....0....2....4
..0....0....3....2....3....3....0....2....1....3....5....1....2....4....1....3
..1....5....4....5....1....0....2....0....3....1....0....2....3....1....1....4
..4....3....5....1....3....1....0....0....0....4....1....1....4....0....2....1

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

Cf. A268327.

Empirical: a(n) = 85*a(n-1) -3366*a(n-2) +82295*a(n-3) -1386925*a(n-4) +17019210*a(n-5) -156331765*a(n-6) +1084941555*a(n-7) -5636724036*a(n-8) +21085378015*a(n-9) -50325001951*a(n-10) +37617575820*a(n-11) +213182974620*a(n-12) -813092997160*a(n-13) +770630574930*a(n-14) +2257030578230*a(n-15) -6653453677281*a(n-16) +247414659915*a(n-17) +21051181958044*a(n-18) -16718457793465*a(n-19) -43997340297789*a(n-20) +53879923261450*a(n-21) +76684670354671*a(n-22) -100035381928785*a(n-23) -126944916371090*a(n-24) +114738194825025*a(n-25) +187188954935145*a(n-26) -51075152814970*a(n-27) -196841758256594*a(n-28) -63278370502380*a(n-29) +98176306220916*a(n-30) +99869982678040*a(n-31) +19690930153560*a(n-32) -26581558465280*a(n-33) -25769657503680*a(n-34) -11894859049920*a(n-35) -3433657832064*a(n-36) -649913978880*a(n-37) -78779602944*a(n-38) -5563468800*a(n-39) -174182400*a(n-40)

A268326 Number of length-(n+1) 0..7 arrays with new values introduced in sequential order, and with new repeated values introduced in sequential order, both starting with zero.

Original entry on oeis.org

2, 4, 11, 33, 114, 435, 1829, 8376, 41466, 220115, 1242614, 7395663, 45999012, 296480813, 1965371333, 13314182333, 91697130971, 639451012407, 4501167824269, 31908164747227, 227399949031725, 1627202389749190, 11680282747792917

Offset: 1

R. H. Hardin, Feb 01 2016

nonn

Column 7 of A268327.

			Some solutions for n=9
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....1....1....0....1....1....1....1....1....1....0....1....1....0
..2....0....2....0....2....1....2....0....2....2....2....0....1....2....0....1
..3....1....1....1....3....1....3....0....1....1....3....0....2....3....2....0
..4....2....3....2....4....0....1....1....0....3....1....0....3....1....3....2
..5....3....1....3....2....2....2....1....3....4....3....0....2....2....2....0
..1....0....4....2....1....3....4....2....0....0....0....2....4....1....4....2
..4....2....1....4....0....4....2....3....3....5....4....0....3....4....2....1
..5....0....5....0....0....1....3....4....2....3....1....3....5....5....1....0
..6....4....4....5....1....5....0....2....3....1....3....4....3....4....2....3

R. H. Hardin, Table of n, a(n) for n = 1..210
R. H. Hardin, Empirical recurrence of order 54

Cf. A268327.

Empirical recurrence of order 54 (see link above)

cp's OEIS Frontend

A268320 Number of length-(n+1) 0..n arrays with new values introduced in sequential order, and with new repeated values introduced in sequential order, both starting with zero.

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A268321 Number of length-(n+1) 0..2 arrays with new values introduced in sequential order, and with new repeated values introduced in sequential order, both starting with zero.

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A268322 Number of length-(n+1) 0..3 arrays with new values introduced in sequential order, and with new repeated values introduced in sequential order, both starting with zero.

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A268323 Number of length-(n+1) 0..4 arrays with new values introduced in sequential order, and with new repeated values introduced in sequential order, both starting with zero.

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A268324 Number of length-(n+1) 0..5 arrays with new values introduced in sequential order, and with new repeated values introduced in sequential order, both starting with zero.

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A268325 Number of length-(n+1) 0..6 arrays with new values introduced in sequential order, and with new repeated values introduced in sequential order, both starting with zero.

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A268326 Number of length-(n+1) 0..7 arrays with new values introduced in sequential order, and with new repeated values introduced in sequential order, both starting with zero.

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