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

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

R. H. Hardin, Table of n, a(n) for n = 1..186

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

Adjacent sequences: A194928 A194929 A194930 * A194932 A194933 A194934

Keyword

nonn,tabl

Author

R. H. Hardin Sep 05 2011

Status

approved