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A200456 Number of -n..n arrays x(0..3) of 4 elements with zero sum and nonzero first and second differences. 1
4, 44, 142, 342, 678, 1148, 1832, 2744, 3874, 5334, 7114, 9192, 11708, 14644, 17962, 21826, 26206, 31044, 36544, 42660, 49310, 56734, 64866, 73616, 83256, 93696, 104834, 116970, 130006, 143824, 158748, 174668, 191446, 209446, 228542, 248572 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row 2 of A200454.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..200

FORMULA

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

Empirical g.f.: 2*(1 + x)*(2 + 18*x + 31*x^2 + 65*x^3 + 63*x^4 + 72*x^5 + 52*x^6 + 39*x^7 + 9*x^8 + 9*x^9) / ((1 - x)^4*(1 + x + x^2)^2*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, May 21 2018

EXAMPLE

Some solutions for n=3:

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

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

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

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

CROSSREFS

Cf. A200454.

Sequence in context: A344871 A071125 A193448 * A292454 A292734 A053314

Adjacent sequences:  A200453 A200454 A200455 * A200457 A200458 A200459

KEYWORD

nonn

AUTHOR

R. H. Hardin, Nov 18 2011

STATUS

approved

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Last modified October 26 05:34 EDT 2021. Contains 348256 sequences. (Running on oeis4.)