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A194931
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
12
2, 3, 8, 4, 17, 64, 5, 26, 217, 1024, 6, 35, 386, 5873, 32768, 7, 44, 557, 12474, 344091, 2097152, 8, 53, 728, 19379, 882318, 43337009, 268435456, 9, 62, 899, 26316, 1481501, 136403494, 11761200209, 68719476736, 10, 71, 1070, 33255, 2089736, 248381815
OFFSET
1,1
COMMENTS
Table starts
...........2.............3..............4..............5...............6
...........8............17.............26.............35..............44
..........64...........217............386............557.............728
........1024..........5873..........12474..........19379...........26316
.......32768........344091.........882318........1481501.........2089736
.....2097152......43337009......136403494......248381815.......364130672
...268435456...11761200209....46128809462....91397735301....139323386328
.68719476736.6872287575297.34125388757746.73818960495633.117075649276412
LINKS
FORMULA
Empirical for rows:
T(1,k) = 1*k + 1
T(2,k) = 9*k - 1
T(3,k) = 171*k - 127 for k>2
T(4,k) = 6939*k - 8379 for k>4
T(5,k) = 609309*k - 956877 for k>6
T(6,k) = 116330103*k - 217580911 for k>8
T(7,k) = 48439766655*k - 102944165347 for k>10
Generalizing, T(n,k) = A141441(n)*k + const(n), for k>2*n-4
CROSSREFS
Sequence in context: A161198 A195232 A093898 * A195248 A229870 A202651
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Sep 05 2011
STATUS
approved