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A212837 Number of 0..n arrays of length 4 with 0 never adjacent to n. 1
2, 41, 178, 497, 1106, 2137, 3746, 6113, 9442, 13961, 19922, 27601, 37298, 49337, 64066, 81857, 103106, 128233, 157682, 191921, 231442, 276761, 328418, 386977, 453026, 527177, 610066, 702353, 804722, 917881, 1042562, 1179521, 1329538 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 3 of A212835.

LINKS

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

FORMULA

Empirical: a(n) = n^4 + 4*n^3 - 4*n + 1.

Conjectures from Colin Barker, Jul 21 2018: (Start)

G.f.: x*(2 + 31*x - 7*x^2 - 3*x^3 + x^4) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)

EXAMPLE

Some solutions for n=5:

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

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

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

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

CROSSREFS

Cf. A212835.

Sequence in context: A088565 A090195 A287335 * A063271 A142160 A174615

Adjacent sequences:  A212834 A212835 A212836 * A212838 A212839 A212840

KEYWORD

nonn

AUTHOR

R. H. Hardin, May 28 2012

STATUS

approved

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Last modified June 15 19:31 EDT 2021. Contains 345049 sequences. (Running on oeis4.)