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 A089934 Table T(n,k) of the number of n X k matrices on {0,1} without adjacent 0's in any row or column. 16
 2, 3, 3, 5, 7, 5, 8, 17, 17, 8, 13, 41, 63, 41, 13, 21, 99, 227, 227, 99, 21, 34, 239, 827, 1234, 827, 239, 34, 55, 577, 2999, 6743, 6743, 2999, 577, 55, 89, 1393, 10897, 36787, 55447, 36787, 10897, 1393, 89, 144, 3363, 39561, 200798, 454385, 454385, 200798 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Recurrence orders are A089935. n X 1/1 X n patterns interpreted as binary values is A003714. Number of independent vertex sets in the P_n X P_k grid graph. - Andrew Howroyd, Jun 06 2017 All columns (or rows) are linear recurrences with constant coefficients and order of the recurrence <= A001224(k+1). - Andrew Howroyd, Dec 24 2019 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..1225 Eric Weisstein's World of Mathematics, Grid Graph Eric Weisstein's World of Mathematics, Independent Vertex Set EXAMPLE Table starts: ======================================================== n\k| 1 2 3 4 5 6 7 ---|---------------------------------------------------- 1 | 2 3 5 8 13 21 34 ... 2 | 3 7 17 41 99 239 577 ... 3 | 5 17 63 227 827 2999 10897 ... 4 | 8 41 227 1234 6743 36787 200798 ... 5 | 13 99 827 6743 55447 454385 3729091 ... 6 | 21 239 2999 36787 454385 5598861 69050253 ... 7 | 34 577 10897 200798 3729091 69050253 1280128950 ... ... - Andrew Howroyd, Jun 06 2017 a(2,2)=7: 11 11 11 10 10 01 01 11 10 01 11 01 11 10 PROG (PARI) step(v, S)={vector(#v, i, sum(j=1, #v, v[j]*!bitand(S[i], S[j])))} mkS(k)={select(b->!bitand(b, b>>1), [0..2^k-1])} T(n, k)={my(S=mkS(k), v=vector(#S, i, i==1)); for(n=1, n, v=step(v, S)); vecsum(v)} \\ Andrew Howroyd, Dec 24 2019 CROSSREFS T(n, 0) = T(0, m) = 1. Zero based table is A089980. Rows 1-7 are A000045, A001333, A051736, A051737, A089936, A089937, A089938. Main diagonal is A006506. Cf. A089935, A001224, A197054 (maximal independent sets), A218354, A003714. Sequence in context: A239586 A180611 A084127 * A113460 A113470 A086786 Adjacent sequences: A089931 A089932 A089933 * A089935 A089936 A089937 KEYWORD nonn,tabl AUTHOR Marc LeBrun, Nov 15 2003 STATUS approved

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Last modified August 8 12:42 EDT 2024. Contains 375021 sequences. (Running on oeis4.)