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A200870 Number of 0..7 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors or less than both neighbors. 1
232, 932, 3704, 14932, 60112, 241718, 971416, 3904290, 15693816, 63085186, 253583656, 1019321774, 4097329180, 16469898636, 66203547550, 266116375576, 1069699742484, 4299838717346, 17283927781406, 69475666835578 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 7 of A200871.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

FORMULA

Empirical: a(n) = 4*a(n-1) -2*a(n-2) +4*a(n-3) +15*a(n-4) +6*a(n-5) +12*a(n-6) +16*a(n-7) +7*a(n-8) +5*a(n-9) +4*a(n-10) +a(n-11).

Empirical g.f.: 2*x*(116 + 2*x + 220*x^2 + 526*x^3 + 292*x^4 + 473*x^5 + 552*x^6 + 257*x^7 + 180*x^8 + 132*x^9 + 32*x^10) / (1 - 4*x + 2*x^2 - 4*x^3 - 15*x^4 - 6*x^5 - 12*x^6 - 16*x^7 - 7*x^8 - 5*x^9 - 4*x^10 - x^11). - Colin Barker, Oct 16 2017

EXAMPLE

Some solutions for n=3

..7....7....7....2....2....2....4....1....6....1....6....0....6....5....7....5

..5....1....5....6....4....2....6....5....2....1....6....0....5....3....3....4

..5....1....5....6....7....4....6....5....0....1....4....1....4....3....2....4

..3....4....4....3....7....7....4....5....0....2....0....1....4....3....1....4

..3....6....0....1....1....7....0....6....7....2....0....3....6....0....1....2

MATHEMATICA

a[0, x_, y_] := 1; a[n_, x_, y_] := a[n, x, y] = Sum[If[z <=x<= y || y <=x<= z, a[n-1, z, x], 0], {z, 8}]; a[n_] := Sum[a[n, x, y], {x, 8}, {y, 8}]; Array[a, 25] (* Giovanni Resta, Mar 05 2014 *)

CROSSREFS

Sequence in context: A245006 A252273 A153466 * A234690 A234683 A238919

Adjacent sequences:  A200867 A200868 A200869 * A200871 A200872 A200873

KEYWORD

nonn

AUTHOR

R. H. Hardin, Nov 23 2011

STATUS

approved

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Last modified October 25 05:57 EDT 2021. Contains 348239 sequences. (Running on oeis4.)