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A068723 Number of solenoidal flows (flow in = flow out) in a 4 X 4 square array with integer velocities -n .. n. 3
1, 2053, 160403, 3096791, 28905785, 173429597, 773568107, 2789847759, 8576204625, 23279942261, 57201104003, 129540052071, 274074872265, 547436323149 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..13.

FORMULA

Empirical G.f.: (x+1)*(x^8 +2042*x^7 +137876*x^6 +1447150*x^5 +3462710*x^4 +1447150*x^3 +137876*x^2 +2042*x +1)/(x-1)^10. [Colin Barker, Jul 31 2012]

EXAMPLE

Sample flows (. represents a space):

Numbers in long rows are on cell walls showing velocity rightward.

Numbers in long columns are on cell floors showing velocity downwards.

4 X 4 cell centers are at the intersection of long rows and long columns.

n=1:

.. 0 . 0 . 0 . 0

.0. -1. -1. -1 . 0

.. 1 . 0 . 0. -1

.0 . 0. -1 . 0 . 0

.. 1 . 1. -1. -1

.0 . 0 . 1 . 0 . 0

.. 1 . 0 . 0. -1

.0 . 1 . 1 . 1 . 0

.. 0 . 0 . 0 . 0

n=2:

.. 0 . 0 . 0 . 0

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

.. 2. -1 . 1. -2

.0 . 0. -2 . 0 . 0

.. 2 . 1. -1. -2

.0 . 0 . 1 . 0 . 0

.. 2 . 0 . 0. -2

.0 . 2 . 2 . 2 . 0

.. 0 . 0 . 0 . 0

CROSSREFS

Cf. 2 X 2=1, 3, 5, 7..., 3 X 3 A068722, 5 X 5 A068724, 6x6 A068725, by velocity limit 1..13 A068726-A068738.

Sequence in context: A238934 A084550 A020400 * A252187 A252509 A250331

Adjacent sequences:  A068720 A068721 A068722 * A068724 A068725 A068726

KEYWORD

nonn

AUTHOR

R. H. Hardin, Feb 26 2002

STATUS

approved

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Last modified April 5 20:13 EDT 2020. Contains 333260 sequences. (Running on oeis4.)