A258734 - OEIS

%I #7 Jan 26 2018 08:50:28

%S 1024,3136,6552,12549,21860,35704,55660,83758,122584,175400,246280,

%T 340263,463524,623564,829420,1091896,1423816,1840300,2359064,3000745,

%U 3789252,4752144,5921036,7332034,9026200,11050048,13456072,16303307

%N Number of length n+4 0..3 arrays with at most one downstep in every n consecutive neighbor pairs.

%C Row 4 of A258730.

%H R. H. Hardin, <a href="/A258734/b258734.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/5040)*n^7 + (1/90)*n^6 + (19/72)*n^5 + (59/18)*n^4 + (47527/720)*n^3 + (14522/45)*n^2 + (39961/84)*n + 100 for n>2.

%F Empirical g.f.: x*(1024 - 5056*x + 10136*x^2 - 9403*x^3 + 988*x^4 + 7460*x^5 - 8940*x^6 + 5164*x^7 - 1576*x^8 + 204*x^9) / (1 - x)^8. - _Colin Barker_, Jan 26 2018

%e Some solutions for n=4:

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

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

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

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

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

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

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

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

%Y Cf. A258730.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jun 08 2015