A194931 - OEIS

%I #6 Dec 18 2015 18:17:44

%S 2,3,8,4,17,64,5,26,217,1024,6,35,386,5873,32768,7,44,557,12474,

%T 344091,2097152,8,53,728,19379,882318,43337009,268435456,9,62,899,

%U 26316,1481501,136403494,11761200209,68719476736,10,71,1070,33255,2089736,248381815

%N T(n,k)=Number of lower triangles of an n X n 0..k array with no element differing from any of its horizontal or vertical neighbors by more than one

%C Table starts

%C ...........2.............3..............4..............5...............6

%C ...........8............17.............26.............35..............44

%C ..........64...........217............386............557.............728

%C ........1024..........5873..........12474..........19379...........26316

%C .......32768........344091.........882318........1481501.........2089736

%C .....2097152......43337009......136403494......248381815.......364130672

%C ...268435456...11761200209....46128809462....91397735301....139323386328

%C .68719476736.6872287575297.34125388757746.73818960495633.117075649276412

%H R. H. Hardin, <a href="/A194931/b194931.txt">Table of n, a(n) for n = 1..186</a>

%F Empirical for rows:

%F T(1,k) = 1*k + 1

%F T(2,k) = 9*k - 1

%F T(3,k) = 171*k - 127 for k>2

%F T(4,k) = 6939*k - 8379 for k>4

%F T(5,k) = 609309*k - 956877 for k>6

%F T(6,k) = 116330103*k - 217580911 for k>8

%F T(7,k) = 48439766655*k - 102944165347 for k>10

%F Generalizing, T(n,k) = A141441(n)*k + const(n), for k>2*n-4

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Sep 05 2011