This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A221596 T(n,k)=Number of 0..k arrays of length n with each element differing from at least one neighbor by 1 or less 9
 0, 0, 4, 0, 7, 8, 0, 10, 17, 16, 0, 13, 26, 49, 32, 0, 16, 35, 100, 139, 64, 0, 19, 44, 169, 342, 393, 128, 0, 22, 53, 256, 651, 1210, 1113, 256, 0, 25, 62, 361, 1068, 2715, 4240, 3151, 512, 0, 28, 71, 484, 1593, 5082, 11011, 14898, 8921, 1024, 0, 31, 80, 625, 2226, 8475 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Table starts ....0......0.......0........0........0.........0.........0.........0..........0 ....4......7......10.......13.......16........19........22........25.........28 ....8.....17......26.......35.......44........53........62........71.........80 ...16.....49.....100......169......256.......361.......484.......625........784 ...32....139.....342......651.....1068......1593......2226......2967.......3816 ...64....393....1210.....2715.....5082......8475.....13056.....18987......26430 ..128...1113....4240....11011....22912.....41401.....67936....103975.....150976 ..256...3151...14898....45099...105586....210101....374342....615965.....954572 ..512...8921...52306...184063...482204...1047967...2006006...3504371....5714456 .1024..25257..183684...752155..2210256...5267759..10894988..20352239...35218688 .2048..71507..645006..3072247.10115926..26387005..58789204.116958723..213700742 .4096.202449.2264978.12550859.46327024.132384353.318224626.675761541.1307528098 LINKS R. H. Hardin, Table of n, a(n) for n = 1..2080 FORMULA Empirical for column k: k=1: a(n) = 2*a(n-1) for n>2 k=2: a(n) = 2*a(n-1) +2*a(n-2) +a(n-3) for n>4 k=3: a(n) = 3*a(n-1) +2*a(n-2) -a(n-3) +a(n-4) k=4: a(n) = 3*a(n-1) +4*a(n-2) +6*a(n-4) +4*a(n-5) +4*a(n-6) k=5: a(n) = 4*a(n-1) +3*a(n-2) -6*a(n-3) +19*a(n-4) +5*a(n-5) +a(n-6) k=6: a(n) = 4*a(n-1) +5*a(n-2) -7*a(n-3) +33*a(n-4) +17*a(n-5) +24*a(n-6) -5*a(n-7) +2*a(n-8) k=7: a(n) = 5*a(n-1) +3*a(n-2) -16*a(n-3) +65*a(n-4) -14*a(n-5) +23*a(n-6) +2*a(n-7) +8*a(n-8) Empirical for row n: n=2: a(n) = 3*n + 1 n=3: a(n) = 9*n - 1 n=4: a(n) = 9*n^2 + 6*n + 1 n=5: a(n) = 54*n^2 - 69*n + 63 for n>2 n=6: a(n) = 27*n^3 + 108*n^2 - 252*n + 267 for n>3 n=7: a(n) = 243*n^3 - 351*n^2 + 237*n + 127 for n>2 EXAMPLE Some solutions for n=6 k=4 ..0....2....3....3....2....2....1....1....2....4....4....2....0....2....4....1 ..0....1....4....2....3....3....2....1....3....3....4....2....1....3....3....2 ..2....4....4....2....1....0....2....3....4....0....4....1....0....2....4....2 ..2....4....1....4....1....0....1....2....0....1....3....4....0....2....4....1 ..0....1....1....3....0....2....2....3....1....4....3....3....1....1....0....0 ..0....2....1....2....1....3....1....2....2....3....2....3....0....1....0....0 CROSSREFS Column 3 is A221568 Row 2 is A016777 Row 3 is A017257(n-1) Row 4 is A016778 Sequence in context: A016682 A198741 A298617 * A195286 A248931 A200501 Adjacent sequences:  A221593 A221594 A221595 * A221597 A221598 A221599 KEYWORD nonn,tabl AUTHOR R. H. Hardin Jan 20 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 14 01:31 EST 2019. Contains 329978 sequences. (Running on oeis4.)