A206450
Number of 0..3 arrays of length n avoiding the consecutive pattern 0..3.
Original entry on oeis.org
4, 16, 64, 255, 1016, 4048, 16128, 64257, 256012, 1020000, 4063872, 16191231, 64508912, 257015648, 1023998720, 4079803649, 16254705684, 64761807088, 258023229632, 1028013114879, 4095797753832, 16318429208240, 65015693603328
Offset: 1
A206451
Number of 0..4 arrays of length n avoiding the consecutive pattern 0..4.
Original entry on oeis.org
5, 25, 125, 625, 3124, 15615, 78050, 390125, 1950000, 9746876, 48718765, 243515775, 1217188750, 6083993750, 30410221874, 152002390605, 759768437250, 3797624997500, 18982040993750, 94879794746876, 474246971343775
Offset: 1
-
M:= <<4|3|3|3|3>,<1|1|1|1|1>,<0|1|0|0|0>,<0|0|1|0|0>,<0|0|0|1|0>>:
seq(<1|1|1|1|1> . M^n . <1,0,0,0,0>, n=1..30); # Robert Israel, Jan 08 2016
A206452
Number of 0..5 arrays of length n avoiding the consecutive pattern 0..5.
Original entry on oeis.org
6, 36, 216, 1296, 7776, 46655, 279924, 1679508, 10076832, 60459696, 362750400, 2176455745, 13058454546, 78349047768, 470084209776, 2820444798960, 16922306043360, 101531659804415, 609176900371944, 3654983053183896
Offset: 1
A206453
Number of 0..6 arrays of length n avoiding the consecutive pattern 0..6.
Original entry on oeis.org
7, 49, 343, 2401, 16807, 117649, 823542, 5764787, 40353460, 282473877, 1977314738, 13841186359, 96888186864, 678216484506, 4747509626755, 33232527033825, 232627406762898, 1628389870025548, 11398715248992477, 79790909854760475
Offset: 1
A206454
Number of 0..7 arrays of length n avoiding the consecutive pattern 0..7.
Original entry on oeis.org
8, 64, 512, 4096, 32768, 262144, 2097152, 16777215, 134217712, 1073741632, 8589932544, 68719456256, 549755617280, 4398044676096, 35184355311616, 281474825715713, 2251798471507992, 18014386698322304, 144115084996645888, 1152920611253710848, 9223364340274069504
Offset: 1
- R. H. Hardin, Table of n, a(n) for n = 1..210
- Index entries for linear recurrences with constant coefficients, signature (8,0,0,0,0,0,0,-1).
-
Table[Sum[(-1)^i*8^(n-8*i)*Binomial[n-7*i,i],{i,0,Floor[n/8]}],{n,20}] (* Stefano Spezia, Feb 12 2023 *)
LinearRecurrence[{8,0,0,0,0,0,0,-1},{8,64,512,4096,32768,262144,2097152,16777215},30] (* Harvey P. Dale, Jan 10 2025 *)
A206456
Number of 0..n arrays of length n+2 avoiding the consecutive pattern 0..n.
Original entry on oeis.org
4, 75, 1016, 15615, 279924, 5764787, 134217712, 3486784383, 99999999980, 3138428376699, 106993205379048, 3937376385699263, 155568095557812196, 6568408355712890595, 295147905179352825824, 14063084452067724990975, 708235345355337676357596, 37589973457545958193355563
Offset: 1
A206457
Number of 0..n arrays of length n+3 avoiding the consecutive pattern 0..n.
Original entry on oeis.org
5, 216, 4048, 78050, 1679508, 40353460, 1073741632, 31381059366, 999999999700, 34522712143568, 1283918464548432, 51185893014090250, 2177953337809370548, 98526125335693358700, 4722366482869645212928, 239072435685151324846286
Offset: 1
A206458
Number of 0..n arrays of length n+4 avoiding the consecutive pattern 0..n.
Original entry on oeis.org
6, 622, 16128, 390125, 10076832, 282473877, 8589932544, 282429533565, 9999999996000, 379749833577917, 15407021574579456, 665416609183171053, 30491346729331184928, 1477891880035400377125, 75557863725914323402752
Offset: 1
A206459
Number of 0..n arrays of length n+5 avoiding the consecutive pattern 0..n.
Original entry on oeis.org
7, 1791, 64257, 1950000, 60459696, 1977314738, 68719456256, 2541865795524, 99999999950000, 4177248169342446, 184884258894932736, 8650415919381195128, 426878854210636550576, 22168378200531005606250, 1208925819614629174378496
Offset: 1
A206460
Number of 0..n arrays of length n+6 avoiding the consecutive pattern 0..n.
Original entry on oeis.org
8, 5157, 256012, 9746876, 362750400, 13841186359, 549755617280, 22876792100667, 999999999400000, 45949729862605855, 2218611106738944000, 112455406951955165371, 5976303958948911170240, 332525673007965083334375
Offset: 1
Showing 1-10 of 11 results.
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