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A229012 T(n,k) = number of arrays of median of three adjacent elements of some length n+2 0..k array, with no adjacent equal elements in the latter. 12
2, 3, 2, 4, 7, 2, 5, 14, 15, 2, 6, 23, 46, 31, 2, 7, 34, 101, 130, 57, 2, 8, 47, 186, 359, 332, 105, 2, 9, 62, 307, 794, 1145, 830, 193, 2, 10, 79, 470, 1527, 3002, 3527, 2054, 353, 2, 11, 98, 681, 2666, 6635, 10860, 10735, 5108, 653, 2, 12, 119, 946, 4335, 13040, 27379 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

.2...3.....4......5......6.......7.......8........9.......10.......11........12

.2...7....14.....23.....34......47......62.......79.......98......119.......142

.2..15....46....101....186.....307.....470......681......946.....1271......1662

.2..31...130....359....794....1527....2666.....4335.....6674.....9839.....14002

.2..57...332...1145...3002....6635...13040....23515....39698....63605.....97668

.2.105...830...3527..10860...27379...60180...119653...220318...381749....629586

.2.193..2054..10735..38768..111311..273124...597477..1197190..2238005...3954490

.2.353..5108..32907.139456..456029.1248872..3004839..6549040.13200731..24974126

.2.653.12790.101635.506236.1888383.5780144.15315095.36345246.79063593.160271154

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..925

FORMULA

Empirical for column k:

k=1: a(n) = a(n-1)

k=2: [order 13]

k=3: [order 27]

k=4: [order 46]

k=5: [order 69]

k=6: [order 95] for n>97

Empirical for row n:

n=1: a(n) = 1*n + 1

n=2: a(n) = 1*n^2 + 2*n - 1

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

n=4: a(n) = (2/3)*n^4 + (10/3)*n^3 - (5/3)*n^2 + (2/3)*n - 1

n=5: [polynomial of degree 5]

n=6: [polynomial of degree 6]

n=7: [polynomial of degree 7]

EXAMPLE

Some solutions for n=4 k=4

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

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

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

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

CROSSREFS

Row 2 is A008865(n+1).

Sequence in context: A079159 A192298 A254967 * A207606 A303845 A132439

Adjacent sequences:  A229009 A229010 A229011 * A229013 A229014 A229015

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Sep 10 2013

STATUS

approved

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Last modified September 29 03:42 EDT 2020. Contains 337420 sequences. (Running on oeis4.)