A068723
Number of solenoidal flows (flow in = flow out) in a 4 X 4 square array with integer velocities -n .. n.
Original entry on oeis.org
1, 2053, 160403, 3096791, 28905785, 173429597, 773568107, 2789847759, 8576204625, 23279942261, 57201104003, 129540052071, 274074872265, 547436323149, 1040787422427, 1895867410719, 3326525754145, 5647051042021, 9308792104563, 14946774417783, 23438233878745, 35975222324029, 54153684727627, 80081666851567, 116509584233329
Offset: 0
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
A068724
Number of solenoidal flows (flow in = flow out) in a 5 X 5 square array with integer velocities -n .. n.
Original entry on oeis.org
1, 569397, 1305759171, 251611610655, 13336307324915, 322309309862183, 4598900066440609, 44976296745414509, 331136639667811845, 1954290045098180729, 9661874271897648847, 41320247284448146619, 156588834507399529975
Offset: 0
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.
5 X 5 cell centers are at the intersection of long rows and long columns.
n=1:
.. 0 . 0 . 0 . 0 . 0
.0. -1. -1. -1. -1 . 0
.. 1 . 0 . 0 . 0. -1
.0 . 0. -1. -1 . 0 . 0
.. 1 . 1 . 0. -1. -1
.0 . 0 . 0 . 0 . 0 . 0
.. 1 . 1 . 0. -1. -1
.0 . 0 . 1 . 1 . 0 . 0
.. 1 . 0 . 0 . 0. -1
.0 . 1 . 1 . 1 . 1 . 0
.. 0 . 0 . 0 . 0 . 0
n=2:
.. 0 . 0 . 0 . 0 . 0
.0. -2. -1. -1. -1 . 0
.. 2. -1 . 0 . 0. -1
.0 . 0. -2. -2. -1 . 0
.. 2 . 1 . 0. -1. -2
.0 . 0. -1. -1 . 0 . 0
.. 2 . 2 . 0. -2. -2
.0 . 0 . 2 . 2 . 0 . 0
.. 2 . 0 . 0 . 0. -2
.0 . 2 . 2 . 2 . 2 . 0
.. 0 . 0 . 0 . 0 . 0
A068752
Number of potential flows in n X n array with integer velocities in -5..5, i.e., number of n X n arrays with adjacent elements differing by no more than 5, counting arrays differing by a constant only once.
Original entry on oeis.org
1, 891, 45642289, 138190481342321, 24953087551680958151267
Offset: 1
A068727
Number of solenoidal flows (flow in = flow out) in an n X n square array with integer velocities in -2 .. 2.
Original entry on oeis.org
1, 5, 247, 160403, 1305759171, 134771061592765, 176541437214450498265, 2940055615889904390546839103, 623112842926151670996790416231139397
Offset: 1
A068728
Number of solenoidal flows (flow in = flow out) in an n X n square array with integer velocities in -3 .. 3.
Original entry on oeis.org
1, 7, 925, 3096791, 251611610655, 500885416261650533, 24461989414349531084868443, 29358790904767905695470325002387331
Offset: 1
A068729
Number of solenoidal flows (flow in = flow out) in an n X n square array with integer velocities in -4 .. 4.
Original entry on oeis.org
1, 9, 2501, 28905785, 13336307324915, 247753867499441888279, 185592614324336736251073584343
Offset: 1
A068730
Number of solenoidal flows (flow in = flow out) in an n X n square array with integer velocities in -5 .. 5.
Original entry on oeis.org
1, 11, 5551, 173429597, 322309309862183, 35922392489639958547367
Offset: 1
A068731
Number of solenoidal flows (flow in = flow out) in an n X n square array with integer velocities in -6 .. 6.
Original entry on oeis.org
1, 13, 10795, 773568107, 4598900066440609, 2286173927365217148894607
Offset: 1
A068732
Number of solenoidal flows (flow in = flow out) in an n X n square array with integer velocities in -7 .. 7.
Original entry on oeis.org
1, 15, 19097, 2789847759, 44976296745414509, 80633423581611695455020595
Offset: 1
A068733
Number of solenoidal flows (flow in = flow out) in an n X n square array with integer velocities in -8 .. 8.
Original entry on oeis.org
1, 17, 31465, 8576204625, 331136639667811845
Offset: 1