# [seqfan] Re: A193376 Tabl = 20 existing sequences

israel at math.ubc.ca israel at math.ubc.ca
Mon Jul 25 06:24:51 CEST 2011

```This satisfies the recursion T(n+2,k) = T(n+1,k) + k T(n,k) with T(0,k) =
1, T(1,k) = 1. Maple's solution is

T(n,k) =
((2 k/(sqrt(1+4 k) - 1))^(n+1) - (-2 k/(sqrt(1+4 k) + 1))^(n+1))/sqrt(1+4
k)

Robert Israel                                israel at math.ubc.ca
Department of Mathematics        http://www.math.ubc.ca/~israel
University of British Columbia            Vancouver, BC, Canada

On Jul 24 2011, Ron Hardin wrote:

> https://oeis.org/A193376 T(n,k)=Number of ways to place any number of 2X1
> tiles of k distinguishable colors into an nX1 grid
>
>
>
> Table starts
> ..1...1....1....1.....1.....1.....1......1......1......1......1......1......1
> ..2...3....4....5.....6.....7.....8......9.....10.....11.....12.....13.....14
> ..3...5....7....9....11....13....15.....17.....19.....21.....23.....25.....27
> ..5..11...19...29....41....55....71.....89....109....131....155....181....209
> ..8..21...40...65....96...133...176....225....280....341....408....481....560
> .13..43...97..181...301...463...673....937...1261...1651...2113...2653...3277
> .21..85..217..441...781..1261..1905...2737...3781...5061...6601...8425..10557
> .34.171..508.1165..2286..4039..6616..10233..15130..21571..29844..40261..53158
> .55.341.1159.2929..6191.11605.19951..32129..49159..72181.102455.141361.190399
> .89.683.2683.7589.17621.35839.66263.113993.185329.287891.430739.624493.881453
> Some solutions for n=5 k=3; colors=1, 2, 3; empty=0
> ..0....2....3....2....0....1....0....0....2....0....0....2....3....0....0....0
> ..0....2....3....2....2....1....2....3....2....1....0....2....3....1....1....1
> ..1....0....0....0....2....0....2....3....2....1....0....1....0....1....1....1
> ..1....2....2....0....3....2....2....3....2....0....3....1....3....3....2....1
> ..0....2....2....0....3....2....2....3....0....0....3....0....3....3....2....1
>
> Possibly interesting because various rows, columns and diagonals are 20
> existing sequences.
>
>
>
>
> rhhardin at mindspring.com
>rhhardin at att.net (either)
>
>
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