A258730 -id:A258730 - cp's OEIS frontend

A258725 Number of length n+3 0..3 arrays with at most one downstep in every 3 consecutive neighbor pairs.

190, 608, 2028, 6552, 20955, 68120, 220854, 711432, 2300008, 7446144, 24054120, 77722752, 251353605, 812507404, 2625900876, 8488906820, 27442096806, 88701621392, 286727659260, 926874621576, 2996101722471, 9684839732128

Offset: 1

R. H. Hardin, Jun 08 2015

nonn

Column 3 of A258730.

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

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

Cf. A258730.

Empirical: a(n) = 4*a(n-1) -6*a(n-2) +20*a(n-3) -34*a(n-4) +24*a(n-5) -16*a(n-6) +8*a(n-7) -a(n-8).

Empirical g.f.: x*(190 - 152*x + 736*x^2 - 1712*x^3 + 1215*x^4 - 836*x^5 + 464*x^6 - 60*x^7) / (1 - 4*x + 6*x^2 - 20*x^3 + 34*x^4 - 24*x^5 + 16*x^6 - 8*x^7 + x^8). - Colin Barker, Jan 26 2018

A258726 Number of length n+4 0..3 arrays with at most one downstep in every 4 consecutive neighbor pairs.

Original entry on oeis.org

512, 1408, 4184, 12549, 35540, 98676, 281136, 819453, 2358888, 6678576, 18944656, 54386801, 156395364, 446683118, 1271579860, 3632749828, 10409795664, 29790138680, 85049570304, 242860722210, 694569186912, 1987109647472

Offset: 1

R. H. Hardin, Jun 08 2015

nonn

Column 4 of A258730

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

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

Cf. A258730

Empirical: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) +30*a(n-4) -72*a(n-5) +58*a(n-6) -16*a(n-7) -31*a(n-8) +36*a(n-9) -10*a(n-10) +a(n-12)

A258727 Number of length n+5 0..3 arrays with at most one downstep in every 5 consecutive neighbor pairs.

Original entry on oeis.org

1212, 2936, 7834, 21860, 59188, 149960, 370510, 941024, 2487276, 6650600, 17371025, 44270908, 112541478, 290771496, 762899717, 1998910152, 5175319416, 13289503784, 34202437664, 88756842476, 231356200114, 601422231744

Offset: 1

R. H. Hardin, Jun 08 2015

nonn

Column 5 of A258730

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

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

Cf. A258730

Empirical: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4) +52*a(n-5) -128*a(n-6) +108*a(n-7) -31*a(n-8) -68*a(n-10) +92*a(n-11) -31*a(n-12) +4*a(n-15) -a(n-16)

A258728 Number of length n+6 0..3 arrays with at most one downstep in every 6 consecutive neighbor pairs.

Original entry on oeis.org

2592, 5664, 13720, 35704, 92548, 228081, 526672, 1183616, 2727288, 6597449, 16454876, 40863000, 98379104, 230053160, 534172704, 1260245516, 3043544240, 7443617220, 18093595536, 43272115712, 102190186552, 241107878575

Offset: 1

R. H. Hardin, Jun 08 2015

nonn

Column 6 of A258730

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

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

Cf. A258730

Empirical: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4) +80*a(n-6) -204*a(n-7) +177*a(n-8) -52*a(n-9) -125*a(n-12) +184*a(n-13) -68*a(n-14) +10*a(n-18) -4*a(n-19)

A258729 Number of length n+7 0..3 arrays with at most one downstep in every 7 consecutive neighbor pairs.

Original entry on oeis.org

5115, 10280, 22866, 55660, 138196, 331584, 752180, 1607656, 3343894, 7100132, 15867680, 37057120, 87647408, 203774064, 457583316, 996246248, 2145967651, 4684383672, 10501666108, 24080284440, 55579151729, 126886388888

Offset: 1

R. H. Hardin, Jun 08 2015

nonn

Column 7 of A258730

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

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

Cf. A258730

Empirical: a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4) +116*a(n-7) -303*a(n-8) +268*a(n-9) -80*a(n-10) -206*a(n-14) +320*a(n-15) -125*a(n-16) +20*a(n-21) -10*a(n-22)

A258731 Number of length n+1 0..3 arrays with at most one downstep in every n consecutive neighbor pairs.

Original entry on oeis.org

16, 60, 190, 512, 1212, 2592, 5115, 9460, 16588, 27820, 44928, 70240, 106760, 158304, 229653, 326724, 456760, 628540, 852610, 1141536, 1510180, 1976000, 2559375, 3283956, 4177044, 5269996, 6598660, 8203840, 10131792, 12434752, 15171497

Offset: 1

R. H. Hardin, Jun 08 2015

nonn

Row 1 of A258730.

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

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

Cf. A258730.

Empirical: a(n) = (1/5040)*n^7 + (1/144)*n^6 + (73/720)*n^5 + (91/144)*n^4 + (179/90)*n^3 + (139/36)*n^2 + (568/105)*n + 4.

Empirical g.f.: x*(2 - x)*(8 - 30*x + 64*x^2 - 80*x^3 + 58*x^4 - 23*x^5 + 4*x^6) / (1 - x)^8. - Colin Barker, Jan 26 2018

A258732 Number of length n+2 0..3 arrays with at most one downstep in every n consecutive neighbor pairs.

Original entry on oeis.org

64, 225, 608, 1408, 2936, 5664, 10280, 17754, 29416, 47047, 72984, 110240, 162640, 234974, 333168, 464474, 637680, 863341, 1154032, 1524624, 1992584, 2578300, 3305432, 4201290, 5297240, 6629139, 8237800, 10169488, 12476448, 15217466

Offset: 1

R. H. Hardin, Jun 08 2015

nonn

Row 2 of A258730.

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

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

Cf. A258730.

Empirical: a(n) = (1/5040)*n^7 + (1/120)*n^6 + (53/360)*n^5 + (5/4)*n^4 + (5167/720)*n^3 + (2489/120)*n^2 + (2591/105)*n + 10.

Empirical g.f.: x*(64 - 287*x + 600*x^2 - 740*x^3 + 576*x^4 - 282*x^5 + 80*x^6 - 10*x^7) / (1 - x)^8. - Colin Barker, Jan 26 2018

A258733 Number of length n+3 0..3 arrays with at most one downstep in every n consecutive neighbor pairs.

Original entry on oeis.org

256, 840, 2028, 4184, 7834, 13720, 22866, 36656, 56925, 86064, 127140, 184032, 261584, 365776, 503914, 684840, 919163, 1219512, 1600812, 2080584, 2679270, 3420584, 4331890, 5444608, 6794649, 8422880, 10375620, 12705168, 15470364

Offset: 1

R. H. Hardin, Jun 08 2015

nonn

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

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

Row 3 of A258730.

Empirical: a(n) = (1/5040)*n^7 + (7/720)*n^6 + (29/144)*n^5 + (305/144)*n^4 + (1027/45)*n^3 + (16267/180)*n^2 + (2425/21)*n + 24 for n>1.

Empirical g.f.: x*(256 - 1208*x + 2476*x^2 - 2856*x^3 + 2026*x^4 - 904*x^5 + 242*x^6 - 32*x^7 + x^8) / (1 - x)^8. - Colin Barker, Jan 26 2018

A258734 Number of length n+4 0..3 arrays with at most one downstep in every n consecutive neighbor pairs.

Original entry on oeis.org

1024, 3136, 6552, 12549, 21860, 35704, 55660, 83758, 122584, 175400, 246280, 340263, 463524, 623564, 829420, 1091896, 1423816, 1840300, 2359064, 3000745, 3789252, 4752144, 5921036, 7332034, 9026200, 11050048, 13456072, 16303307

Offset: 1

R. H. Hardin, Jun 08 2015

nonn

Row 4 of A258730.

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

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

Cf. A258730.

Empirical: a(n) = (1/5040)*n^7 + (1/90)*n^6 + (19/72)*n^5 + (59/18)*n^4 + (47527/720)*n^3 + (14522/45)*n^2 + (39961/84)*n + 100 for n>2.

Empirical g.f.: x*(1024 - 5056*x + 10136*x^2 - 9403*x^3 + 988*x^4 + 7460*x^5 - 8940*x^6 + 5164*x^7 - 1576*x^8 + 204*x^9) / (1 - x)^8. - Colin Barker, Jan 26 2018

A258735 Number of length n+5 0..3 arrays with at most one downstep in every n consecutive neighbor pairs.

Original entry on oeis.org

4096, 11704, 20955, 35540, 59188, 92548, 138196, 199264, 279560, 383704, 517281, 687012, 900944, 1168660, 1501510, 1912864, 2418388, 3036344, 3787915, 4697556, 5793372, 7107524, 8676664, 10542400, 12751792, 15357880, 18420245, 22005604

Offset: 1

R. H. Hardin, Jun 08 2015

nonn

Row 5 of A258730.

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

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

Cf. A258730.

Empirical: a(n) = (1/5040)*n^7 + (1/80)*n^6 + (241/720)*n^5 + (229/48)*n^4 + (15569/90)*n^3 + (58693/60)*n^2 + (175526/105)*n + 512 for n>3.

Empirical g.f.: x*(4096 - 21064*x + 42011*x^2 - 33764*x^3 - 7096*x^4 + 30588*x^5 - 9050*x^6- 20224*x^7 + 22372*x^8 - 9344*x^9 + 1476*x^10) / (1 - x)^8. - Colin Barker, Jan 26 2018

cp's OEIS Frontend

A258725 Number of length n+3 0..3 arrays with at most one downstep in every 3 consecutive neighbor pairs.

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A258726 Number of length n+4 0..3 arrays with at most one downstep in every 4 consecutive neighbor pairs.

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A258727 Number of length n+5 0..3 arrays with at most one downstep in every 5 consecutive neighbor pairs.

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A258728 Number of length n+6 0..3 arrays with at most one downstep in every 6 consecutive neighbor pairs.

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A258729 Number of length n+7 0..3 arrays with at most one downstep in every 7 consecutive neighbor pairs.

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A258731 Number of length n+1 0..3 arrays with at most one downstep in every n consecutive neighbor pairs.

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A258732 Number of length n+2 0..3 arrays with at most one downstep in every n consecutive neighbor pairs.

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A258733 Number of length n+3 0..3 arrays with at most one downstep in every n consecutive neighbor pairs.

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A258734 Number of length n+4 0..3 arrays with at most one downstep in every n consecutive neighbor pairs.

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