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A203094 Number of nX1 0..3 arrays with every nonzero element less than or equal to some horizontal or vertical neighbor. 8

%I #15 Jul 18 2023 12:26:26

%S 1,4,16,50,144,422,1268,3823,11472,34350,102896,308419,924532,2771101,

%T 8305373,24892609,74608516,223618304,670231838,2008825312,6020872062,

%U 18045827096,54087163859,162110668160,485879938474,1456284886944

%N Number of nX1 0..3 arrays with every nonzero element less than or equal to some horizontal or vertical neighbor.

%H R. H. Hardin, <a href="/A203094/b203094.txt">Table of n, a(n) for n = 1..210</a>

%H T. Mansour and M. Shattuck, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Shattuck/shattuck3.html">Counting Peaks and Valleys in a Partition of a Set</a>, J. Int. Seq. 13 (2010), 10.6.8, Lemma 2.1, k=4, no peak.

%F Empirical: a(n) = 4*a(n-1) -6*a(n-2) +10*a(n-3) -5*a(n-4) +6*a(n-5) -a(n-6) +a(n-7).

%F Empirical: G.f.: -x*(1+6*x^2+5*x^4+x^6) / (-1+4*x-6*x^2+10*x^3-5*x^4+6*x^5-x^6+x^7). - _R. J. Mathar_, May 17 2014

%e Some solutions for n=5

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

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

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

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

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

%Y Column 1 of A203101. Also a column of A228461. Cf. A217883, A217954.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 29 2011

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)