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A200886 T(n,k)=Number of 0..k arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors 13
7, 22, 12, 50, 51, 21, 95, 144, 121, 37, 161, 325, 422, 292, 65, 252, 636, 1121, 1268, 704, 114, 372, 1127, 2507, 3985, 3823, 1691, 200, 525, 1856, 4977, 10213, 14288, 11472, 4059, 351, 715, 2889, 9052, 22736, 42182, 50995, 34350, 9749, 616, 946, 4300, 15393 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

....7....22.....50......95......161.......252.......372........525........715

...12....51....144.....325......636......1127......1856.......2889.......4300

...21...121....422....1121.....2507......4977......9052......15393......24817

...37...292...1268....3985....10213.....22736.....45648......84681.....147565

...65...704...3823...14288....42182....105813....235538.....478467.....904111

..114..1691..11472...50995...173606....491533...1215616....2710413....5567530

..200..4059..34350..181336...710976...2269938...6233356...15250675...34054592

..351..9749.102896..644721..2908797..10462235..31868448...85473225..207289059

..616.23422.308419.2294193.11911516..48259083.163014678..479101189.1261310492

.1081.56268.924532.8166441.48807427.222798408.834763824.2688814689.7684922749

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..9999

FORMULA

Empirical for columns:

k=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3)

k=2: a(n) = 3*a(n-1) -3*a(n-2) +4*a(n-3) -a(n-4) +a(n-5)

k=3: 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)

k=4: a(n) = 5*a(n-1) -10*a(n-2) +20*a(n-3) -15*a(n-4) +21*a(n-5) -7*a(n-6) +8*a(n-7) -a(n-8) +a(n-9)

k=5: a(n) = 6*a(n-1) -15*a(n-2) +35*a(n-3) -35*a(n-4) +56*a(n-5) -28*a(n-6) +36*a(n-7) -9*a(n-8) +10*a(n-9) -a(n-10) +a(n-11)

k=6: a(n) = 7*a(n-1) -21*a(n-2) +56*a(n-3) -70*a(n-4) +126*a(n-5) -84*a(n-6) +120*a(n-7) -45*a(n-8) +55*a(n-9) -11*a(n-10) +12*a(n-11) -a(n-12) +a(n-13)

k=7: a(n) = 8*a(n-1) -28*a(n-2) +84*a(n-3) -126*a(n-4) +252*a(n-5) -210*a(n-6) +330*a(n-7) -165*a(n-8) +220*a(n-9) -66*a(n-10) +78*a(n-11) -13*a(n-12) +14*a(n-13) -a(n-14) +a(n-15)

Empirical for rows:

n=1: a(k) = (2/3)*k^3 + (5/2)*k^2 + (17/6)*k + 1

n=2: a(k) = (1/3)*k^4 + (7/3)*k^3 + (14/3)*k^2 + (11/3)*k + 1

n=3: a(k) = (2/15)*k^5 + (11/6)*k^4 + (35/6)*k^3 + (23/3)*k^2 + (68/15)*k + 1

n=4: a(k) = (2/45)*k^6 + (19/15)*k^5 + (217/36)*k^4 + (71/6)*k^3 + (2057/180)*k^2 + (27/5)*k + 1

n=5: a(k) = (4/315)*k^7 + (7/9)*k^6 + (241/45)*k^5 + (1067/72)*k^4 + (3757/180)*k^3 + (1145/72)*k^2 + (2629/420)*k + 1

n=6: a(k) = (1/315)*k^8 + (134/315)*k^7 + (21/5)*k^6 + (571/36)*k^5 + (1841/60)*k^4 + (6047/180)*k^3 + (26603/1260)*k^2 + (299/42)*k + 1

n=7: a(k) = (2/2835)*k^9 + (131/630)*k^8 + (2803/945)*k^7 + (1349/90)*k^6 + (41449/1080)*k^5 + (20423/360)*k^4 + (1149293/22680)*k^3 + (22741/840)*k^2 + (2011/252)*k + 1

EXAMPLE

Some solutions for n=4 k=3

..1....2....3....0....0....1....2....3....0....1....2....3....3....1....2....2

..1....2....1....0....1....0....1....0....3....0....2....2....3....0....3....2

..2....2....3....0....2....2....3....2....3....0....3....3....3....1....3....0

..2....0....3....0....3....3....3....3....2....0....3....3....3....1....0....2

..1....1....2....1....3....3....2....3....0....1....3....3....3....1....2....3

..0....2....2....1....3....2....1....0....2....1....2....1....1....3....3....3

CROSSREFS

Column 1 is A005251(n+5)

Row 1 is A002412(n+1)

Sequence in context: A130740 A101119 A217014 * A070412 A286572 A055575

Adjacent sequences:  A200883 A200884 A200885 * A200887 A200888 A200889

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Nov 23 2011

STATUS

approved

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Last modified March 22 04:32 EDT 2019. Contains 321406 sequences. (Running on oeis4.)