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A281767 Number of 3Xn 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards. 1

%I #4 Jan 29 2017 12:42:08

%S 0,10,47,152,609,2138,7466,25798,87397,293470,979311,3235714,10650401,

%T 34842532,113507950,368400482,1191351902,3841448788,12352142633,

%U 39620840414,126807886700,405026431154,1291283976919,4109819232304

%N Number of 3Xn 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

%C Row 3 of A281765.

%H R. H. Hardin, <a href="/A281767/b281767.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) +7*a(n-2) -80*a(n-3) -60*a(n-4) +610*a(n-5) +488*a(n-6) -2954*a(n-7) -2778*a(n-8) +9782*a(n-9) +10423*a(n-10) -24116*a(n-11) -27411*a(n-12) +46820*a(n-13) +54750*a(n-14) -74006*a(n-15) -87429*a(n-16) +97522*a(n-17) +114272*a(n-18) -108436*a(n-19) -124098*a(n-20) +102206*a(n-21) +112813*a(n-22) -81722*a(n-23) -85782*a(n-24) +55064*a(n-25) +54233*a(n-26) -30842*a(n-27) -28193*a(n-28) +14078*a(n-29) +11842*a(n-30) -5088*a(n-31) -3915*a(n-32) +1398*a(n-33) +977*a(n-34) -274*a(n-35) -172*a(n-36) +34*a(n-37) +19*a(n-38) -2*a(n-39) -a(n-40) for n>41

%e Some solutions for n=4

%e ..0..0..1..0. .0..0..1..1. .0..0..0..1. .0..0..1..1. .0..1..1..1

%e ..1..1..0..0. .1..1..0..1. .1..1..1..0. .0..1..0..1. .1..1..1..1

%e ..1..1..0..0. .0..0..1..0. .1..1..0..1. .1..0..1..1. .1..1..1..1

%Y Cf. A281765.

%K nonn

%O 1,2

%A _R. H. Hardin_, Jan 29 2017

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Last modified July 18 03:34 EDT 2024. Contains 374377 sequences. (Running on oeis4.)