A223876 - OEIS

%I #4 Mar 28 2013 10:19:12

%S 4,16,16,50,256,64,130,2500,4096,256,296,16900,99223,65536,1024,610,

%T 87616,1336985,3863372,1048576,4096,1163,372100,12520369,88682677,

%U 152918517,16777216,16384,2083,1352569,90648289,1271992512,5941888105

%N T(n,k)=Number of nXk 0..3 arrays with rows, diagonals and antidiagonals unimodal

%C Table starts

%C .......4............16................50..................130

%C ......16...........256..............2500................16900

%C ......64..........4096.............99223..............1336985

%C .....256.........65536...........3863372.............88682677

%C ....1024.......1048576.........152918517...........5941888105

%C ....4096......16777216........6066668157.........411716468431

%C ...16384.....268435456......240345697904.......28928809433978

%C ...65536....4294967296.....9519219712534.....2033941972287214

%C ..262144...68719476736...377068749332794...142745781634483746

%C .1048576.1099511627776.14936662560715369.10010372252279889400

%H R. H. Hardin, <a href="/A223876/b223876.txt">Table of n, a(n) for n = 1..97</a>

%F Empirical for column k:

%F k=1: a(n) = 4*a(n-1)

%F k=2: a(n) = 16*a(n-1)

%F k=3: [recurrence of order 28]

%F Empirical: rows n=1..4 are polynomials of degree 6*n for k>0,0,1,10

%e Some solutions for n=3 k=4

%e ..0..0..0..1....0..0..0..3....0..2..3..3....0..0..0..2....0..0..0..0

%e ..2..2..2..3....2..2..3..3....2..2..3..1....0..2..2..2....0..0..0..3

%e ..2..3..1..1....0..1..2..3....1..1..3..1....2..2..2..1....1..1..3..1

%Y Column 1 is A000302

%Y Column 2 is A001025

%Y Row 1 is A223659

%Y Row 2 is A223756

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_ Mar 28 2013