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A068722 Number of solenoidal flows (flow in = flow out) in a 3 X 3 square array with integer velocities -n .. n. 36
1, 35, 247, 925, 2501, 5551, 10795, 19097, 31465, 49051, 73151, 105205, 146797, 199655, 265651, 346801, 445265, 563347, 703495, 868301, 1060501, 1282975, 1538747, 1830985, 2163001, 2538251, 2960335, 3432997, 3960125, 4545751 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Conjecture: A255437(a(n)) = 2*n+1, i.e. a(n) = gives the position of the first occurrence of 2*n+1 in A255437. - Reinhard Zumkeller, Mar 23 2015

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

FORMULA

a(n) = (1+2*n+2*n^2) * (1+3*n+3*n^2).

G.f.: (1+30*x+82*x^2+30*x^3+x^4)/(1-x)^5. - Colin Barker, Jul 30 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.

3 X 3 cell centers are at the intersection of long rows and long columns.

n=1:

.. 0 . 0 . 0

.0. -1. -1 . 0

.. 1 . 0. -1

.0 . 0 . 0 . 0

.. 1 . 0. -1

.0 . 1 . 1 . 0

.. 0 . 0 . 0

n=2:

.. 0 . 0 . 0

.0. -2. -1 . 0

.. 2. -1. -1

.0 . 0. -1 . 0

.. 2 . 0. -2

.0 . 2 . 2 . 0

.. 0 . 0 . 0

PROG

(Haskell)

a068722 n = (1 + 2 * n + 2 * n ^ 2) * (1 + 3 * n + 3 * n ^ 2)

-- Reinhard Zumkeller, Mar 23 2015

(PARI) a(n)=(1+2*n+2*n^2)*(1+3*n+3*n^2) \\ Charles R Greathouse IV, Apr 08 2016

CROSSREFS

Cf. 2 X 2=1, 3, 5, 7..., 4 X 4 A068723, 5 X 5 A068724, 6x6 A068725, by velocity limit 1..13 A068726-A068738.

Cf. A016754, A255437.

Sequence in context: A223648 A219474 A220208 * A255584 A113941 A067238

Adjacent sequences:  A068719 A068720 A068721 * A068723 A068724 A068725

KEYWORD

nonn,easy

AUTHOR

R. H. Hardin, Feb 26 2002

EXTENSIONS

Formula corrected by Colin Barker, Jul 30 2012

STATUS

approved

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Last modified February 26 21:53 EST 2020. Contains 332295 sequences. (Running on oeis4.)