cp's OEIS Frontend

A295275 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 1 or 4 1s.

%I A295275 #8 Oct 20 2023 15:04:09
%S A295275 2,4,4,7,11,7,13,33,33,13,24,98,164,98,24,44,291,811,811,291,44,81,
%T A295275 865,4035,6659,4035,865,81,149,2570,19997,54773,54773,19997,2570,149,
%U A295275 274,7637,99245,449827,748740,449827,99245,7637,274,504,22693,492401,3697742
%N A295275 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 1 or 4 1s.
%C A295275 Table starts
%C A295275 ...2.....4.......7........13..........24............44..............81
%C A295275 ...4....11......33........98.........291...........865............2570
%C A295275 ...7....33.....164.......811........4035.........19997...........99245
%C A295275 ..13....98.....811......6659.......54773........449827.........3697742
%C A295275 ..24...291....4035.....54773......748740......10203847.......139221499
%C A295275 ..44...865...19997....449827....10203847.....230659662......5221177246
%C A295275 ..81..2570...99245...3697742...139221499....5221177246....196091375073
%C A295275 .149..7637..492401..30386185..1898916677..118139247475...7361533108317
%C A295275 .274.22693.2443097.249719021.25902054180.2673342943199.276386201580189
%H A295275 R. H. Hardin, <a href="/A295275/b295275.txt">Table of n, a(n) for n = 1..419</a>
%F A295275 Empirical for column k:
%F A295275 k=1: a(n) = a(n-1) +a(n-2) +a(n-3)
%F A295275 k=2: a(n) = 2*a(n-1) +3*a(n-2) -a(n-4)
%F A295275 k=3: [order 10]
%F A295275 k=4: [order 16]
%F A295275 k=5: [order 40]
%F A295275 k=6: [order 78]
%e A295275 Some solutions for n=4 k=4
%e A295275 ..1..0..1..0....0..0..0..1....1..0..1..0....0..1..1..0....0..0..0..0
%e A295275 ..0..1..1..1....0..0..1..0....1..0..1..0....0..0..0..1....0..1..0..1
%e A295275 ..0..0..1..0....0..0..0..1....0..0..0..0....1..0..0..1....0..0..1..0
%e A295275 ..1..0..0..0....1..1..0..0....0..1..1..0....0..1..1..0....1..1..0..0
%Y A295275 Columns are A000073(n+3), A282990, A295270, A295271, A295272, A295273, A295274.
%Y A295275 Diagonal is A295269.
%K A295275 nonn,tabl
%O A295275 1,1
%A A295275 _R. H. Hardin_, Nov 19 2017