The On-Line Encyclopedia of Integer Sequences (OEIS)

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A200836

Number of 0..6 arrays x(0..n+1) of n+2 elements without any two consecutive increases or two consecutive decreases.
(history; published version)

#10 by N. J. A. Sloane at Sun Oct 15 20:28:37 EDT 2017

STATUS

proposed

approved

#9 by Michel Marcus at Sun Oct 15 14:58:07 EDT 2017

STATUS

editing

proposed

#8 by Michel Marcus at Sun Oct 15 14:58:03 EDT 2017

AUTHOR

R. H. Hardin , Nov 23 2011

STATUS

proposed

editing

#7 by Colin Barker at Sun Oct 15 12:48:34 EDT 2017

STATUS

editing

proposed

#6 by Colin Barker at Sun Oct 15 12:48:17 EDT 2017

NAME

Number of 0..6 arrays x(0..n+1) of n+2 elements without any two consecutive increases or two consecutive decreases.

COMMENTS

Column 6 of A200838.

FORMULA

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

Empirical g.f.: x*(273 - 420*x + 259*x^2 - 427*x^3 + 320*x^4 - 319*x^5 + 236*x^6 - 91*x^7 + 49*x^8) / (1 - 7*x + 9*x^2 - 6*x^3 + 9*x^4 - 7*x^5 + 7*x^6 - 5*x^7 + 2*x^8 - x^9). - Colin Barker, Oct 15 2017

STATUS

approved

editing

#5 by Russ Cox at Sat Mar 31 12:36:41 EDT 2012

AUTHOR

_R. H. Hardin (rhhardin(AT)att.net) _ Nov 23 2011

Discussion

Sat Mar 31

12:36

OEIS Server: https://oeis.org/edit/global/875

#4 by Ron Hardin at Wed Nov 23 06:41:50 EST 2011

STATUS

editing

approved

#3 by Ron Hardin at Wed Nov 23 06:41:41 EST 2011

LINKS

R. H. Hardin, <a href="/A200836/b200836.txt">Table of n, a(n) for n = 1..210</a>

#2 by Ron Hardin at Wed Nov 23 06:41:11 EST 2011

NAME

allocated for Ron HardinNumber of 0..6 arrays x(0..n+1) of n+2 elements without any two consecutive increases or two consecutive decreases

DATA

273, 1491, 8239, 45465, 250913, 1384813, 7642875, 42181611, 232803603, 1284861277, 7091249941, 39137163521, 216001069269, 1192126810953, 6579441195743, 36312451033865, 200411259993515, 1106085433196691

OFFSET

1,1

COMMENTS

Column 6 of A200838

FORMULA

Empirical: a(n) = 7*a(n-1) -9*a(n-2) +6*a(n-3) -9*a(n-4) +7*a(n-5) -7*a(n-6) +5*a(n-7) -2*a(n-8) +a(n-9)

EXAMPLE

Some solutions for n=3

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

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

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

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

..4....5....3....5....4....1....6....3....5....3....4....3....6....5....6....3

KEYWORD

allocated

nonn

AUTHOR

R. H. Hardin (rhhardin(AT)att.net) Nov 23 2011

STATUS

approved

editing

#1 by Ron Hardin at Wed Nov 23 06:35:23 EST 2011

NAME

allocated for Ron Hardin

KEYWORD

allocated

STATUS

approved