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 A302069 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2 or 4 horizontally or antidiagonally adjacent elements, with upper left element zero. 12
 1, 2, 2, 4, 8, 4, 8, 25, 32, 8, 16, 81, 148, 128, 16, 32, 263, 748, 884, 512, 32, 64, 855, 3657, 7070, 5296, 2048, 64, 128, 2778, 18108, 54177, 67070, 31760, 8192, 128, 256, 9027, 89658, 420121, 807601, 636852, 190528, 32768, 256, 512, 29333, 444359 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Table starts ...1......2.......4.........8..........16............32..............64 ...2......8......25........81.........263...........855............2778 ...4.....32.....148.......748........3657.........18108...........89658 ...8....128.....884......7070.......54177........420121.........3247765 ..16....512....5296.....67070......807601.......9825815.......119508742 ..32...2048...31760....636852....12063625.....230634314......4418931065 ..64...8192..190528...6048836...180330117....5420105343....163660519064 .128..32768.1143104..57457232..2696254757..127431664603...6065045335103 .256.131072.6858496.545796112.40316943551.2996509042607.224815724811979 LINKS R. H. Hardin, Table of n, a(n) for n = 1..311 FORMULA Empirical for column k: k=1: a(n) = 2*a(n-1) k=2: a(n) = 4*a(n-1) k=3: a(n) = 8*a(n-1) -12*a(n-2) for n>3 k=4: a(n) = 16*a(n-1) -76*a(n-2) +148*a(n-3) -124*a(n-4) +36*a(n-5) for n>6 k=5: [order 11] for n>13 k=6: [order 25] for n>27 k=7: [order 53] for n>56 Empirical for row n: n=1: a(n) = 2*a(n-1) n=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4) for n>6 n=3: [order 15] for n>18 n=4: [order 53] for n>58 EXAMPLE Some solutions for n=5 k=4 ..0..1..0..0. .0..1..0..0. .0..0..1..1. .0..1..1..0. .0..1..0..0 ..1..0..0..0. .1..1..1..0. .0..1..0..0. .1..0..1..0. .0..1..1..1 ..1..0..1..0. .0..1..1..0. .0..0..1..0. .0..1..0..1. .1..0..1..0 ..1..1..1..0. .0..0..1..0. .1..1..1..0. .1..0..1..0. .0..0..1..0 ..1..1..0..1. .1..0..1..1. .1..1..0..1. .0..0..0..1. .0..0..1..0 CROSSREFS Column 1 is A000079(n-1). Column 2 is A004171(n-1). Row 1 is A000079(n-1). Row 2 is A301842. Sequence in context: A299180 A299942 A301841 * A298195 A299089 A299345 Adjacent sequences: A302066 A302067 A302068 * A302070 A302071 A302072 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Mar 31 2018 STATUS approved

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Last modified March 29 18:41 EDT 2023. Contains 361599 sequences. (Running on oeis4.)