A067965
Number of binary arrangements without adjacent 1's on n X n array connected ne-sw and nw-se.
Original entry on oeis.org
2, 9, 119, 2704, 177073, 21836929, 6985036032, 4576976735769, 7263963336910751, 24830487842030082304, 198126078679714777857441, 3494153303407491549112098721, 141264727800378056245286463971328, 12779122891585386852029424628087941481, 2628141044813862018744988536642011269669959
Offset: 1
Neighbors for n=4 (dots represent spaces):
. o..o..o..o
...\/ \/ \/
.../\ /\ /\
. o..o..o..o
...\/ \/ \/
.../\ /\ /\
. o..o..o..o
...\/ \/ \/
.../\ /\ /\
. o..o..o..o
Cf. circle
A000204, line
A000045, arrays: e-w ne-sw nw-se
A067963, n-s nw-se
A067964, e-w n-s nw-se
A066864, e-w ne-sw n-s nw-se
A063443, n-s
A067966, e-w n-s
A006506, nw-se
A067962, toruses: bare
A002416, ne-sw nw-se
A067960, ne-sw n-s nw-se
A067959, e-w ne-sw n-s nw-se
A067958, n-s
A067961, e-w n-s
A027683, e-w ne-sw n-s
A066866.
A181207
Number of n X 3 binary matrices with no two 1's adjacent diagonally or antidiagonally.
Original entry on oeis.org
8, 25, 119, 484, 2117, 9025, 38936, 167281, 720083, 3097600, 13329209, 57350329, 246768392, 1061782225, 4568619071, 19657722436, 84582794333, 363940725625, 1565955363224, 6737954403049, 28991906279867, 124745667481600
Offset: 1
A181208
Number of n X 4 binary matrices with no two 1's adjacent diagonally or antidiagonally.
Original entry on oeis.org
16, 64, 484, 2704, 17424, 104976, 652864, 4000000, 24681024, 151782400, 934891776, 5754132736, 35428274176, 218096472064, 1342706197504, 8266039005184, 50888705511424, 313286601609216, 1928696564957184, 11873676328960000
Offset: 1
-
f:= gfun:-rectoproc({a(n)=6*a(n-1)+8*a(n-2)-48*a(n-3)+24*a(n-4)+32*a(n-5)-16*a(n-6), a(1)=16, a(2)=64, a(3)=484, a(4)=2704, a(5)=17424, a(6)=104976},a(n),remember):
map(f, [$1..20]); # Robert Israel, Dec 25 2017
-
RecurrenceTable[{a[n] == 6*a[n-1] + 8*a[n-2] - 48*a[n-3] + 24*a[n-4] + 32*a[n-5] - 16*a[n-6], a[1] == 16, a[2] == 64, a[3] == 484, a[4] == 2704, a[5] == 17424, a[6] == 104976}, a, {n, 1, 20}] (* Jean-François Alcover, Aug 29 2022, after Robert Israel *)
LinearRecurrence[{6,8,-48,24,32,-16},{16,64,484,2704,17424,104976},30] (* Harvey P. Dale, Aug 29 2024 *)
-
Vec(4*x*(4 - 8*x - 7*x^2 + 14*x^3 + 4*x^4 - 4*x^5) / ((1 - 8*x + 12*x^2 - 4*x^3)*(1 + 2*x - 4*x^2 - 4*x^3)) + O(x^30)) \\ Colin Barker, Mar 26 2018
A181209
Number of n X 5 binary matrices with no two 1's adjacent diagonally or antidiagonally.
Original entry on oeis.org
32, 169, 2117, 17424, 177073, 1630729, 15786848, 149352841, 1429585373, 13610488896, 129934154497, 1238878076401, 11819811992192, 112736763711049, 1075437390934037, 10258292274099984, 97854335246290033, 933422273708422969
Offset: 1
- Robert Israel, Table of n, a(n) for n = 1..1019 (n = 1..250 from R. H. Hardin)
- Robert Israel, Maple-assisted proof of formula
- Index entries for linear recurrences with constant coefficients, signature (12, 0, -283, 516, 600, -1415, 0, 600, -125).
-
f:= gfun:-rectoproc({a(n)=12*a(n-1)-283*a(n-3)+516*a(n-4)+600*a(n-5)-1415*a(n-6)+600*a(n-8)-125*a(n-9),a(1) = 32, a(2) = 169, a(3) = 2117, a(4) = 17424, a(5) = 177073, a(6) = 1630729, a(7) = 15786848, a(8) = 149352841,a(9)=1429585373},a(n),remember):
map(f, [$1..30]); # Robert Israel, Dec 25 2017
-
RecurrenceTable[{a[n] == 12*a[n - 1] - 283*a[n - 3] + 516*a[n - 4] + 600*a[n - 5] - 1415*a[n - 6] + 600*a[n - 8] - 125*a[n - 9], a[1] == 32, a[2] == 169, a[3] == 2117, a[4] == 17424, a[5] == 177073, a[6] == 1630729, a[7] == 15786848, a[8] == 149352841, a[9] == 1429585373}, a, {n, 1, 30}] (* Jean-François Alcover, Aug 29 2022, after Robert Israel *)
A181210
Number of nX6 binary matrices with no two 1's adjacent diagonally or antidiagonally.
Original entry on oeis.org
64, 441, 9025, 104976, 1630729, 21836929, 315701824, 4388400025, 62249751001, 873880953856, 12333757683025, 173597094140625, 2446840043215936, 34462915406893801, 485580777431805169, 6840488501157755536
Offset: 1
A181211
Number of nX7 binary matrices with no two 1's adjacent diagonally or antidiagonally.
Original entry on oeis.org
128, 1156, 38936, 652864, 15786848, 315701824, 6985036032, 146719641600, 3168621039616, 67463750631424, 1447364588320768, 30930859081810944, 662387735874816000, 14169961476541661184, 303300655391773020160
Offset: 1
Showing 1-6 of 6 results.
Comments