A197458 -id:A197458 - cp's OEIS frontend

A007107 Number of labeled 2-regular digraphs with n nodes.

1, 0, 0, 1, 9, 216, 7570, 357435, 22040361, 1721632024, 166261966956, 19459238879565, 2714812050902545, 445202898702992496, 84798391618743138414, 18567039007438379656471, 4631381194792101913679985, 1305719477625154539392776080, 413153055417968797025496881656

Offset: 0

N. J. A. Sloane

Or number of n X n matrices with exactly two 1's in each row and column which are not in the main diagonal, other entries 0 (cf. A001499). - Vladimir Shevelev, Mar 22 2010

Number of 2-factors of the n-crown graph. - Andrew Howroyd, Feb 28 2016

R. W. Robinson, personal communication.
R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1982.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Alois P. Heinz, Table of n, a(n) for n = 0..254 (first 49 terms from R. W. Robinson)
O. Gonzalez, C. Beltran and I. Santamaria, On the Number of Interference Alignment Solutions for the K-User MIMO Channel with Constant Coefficients, arXiv preprint arXiv:1301.6196 [cs.IT], 2013. - From _N. J. A. Sloane_, Feb 19 2013
R. J. Mathar, OEIS A007107, Mar 15 2019

Cf. column t=0 of A284989.

Cf. A007108 (log transform), A197458 (row and column sum <=2), A219889 (unlabeled), A001499 (loops allowed).

a:= proc(n) option remember; `if`(n<5, ((n-1)*(n-2)/2)^2,
      (n-1)*(2*(n^3-2*n^2+n+1)*a(n-1)/(n-2)+((n^2-2*n+2)*
      (n+1)*a(n-2) +(2*n^2-6*n+1)*n*a(n-3)+(n-3)*(a(n-4)*
      (n^3-5*n^2+3)-(n-4)*(n-1)*(n+1)*a(n-5))))/(2*n))
    end:
seq(a(n), n=0..20);  # Alois P. Heinz, Apr 10 2017

Table[Sum[Sum[Sum[(-1)^(k+j-s)*n!*(n-k)!*(2n-k-2j-s)!/(s!*(k-s)!*(n-k-j)!^2*j!*2^(2n-2k-j)),{j,0,n-k}],{s,0,k}],{k,0,n}],{n,0,20}] (* Vaclav Kotesovec, May 09 2014 after Shanzhen Gao *)

a(n)=sum(k=0,n, sum(s=0,k, sum(j=0,n-k, (-1)^(k+j-s)*n!*(n-k)!*(2*n-k-2*j-s)!/(s!*(k-s)!*(n-k-j)!^2*j!*2^(2*n-2*k-j))))) \\ Charles R Greathouse IV, Feb 08 2017

a(n) = Sum_{k=0..n} Sum_{s=0..k} Sum_{j=0..n-k} (-1)^(k+j-s)*n!*(n-k)!*(2n-k-2j-s)!/(s!*(k-s)!*(n-k-j)!^2*j!*2^(2n-2k-j)). - Shanzhen Gao, Nov 05 2007

a(n) ~ 2*sqrt(Pi) * n^(2*n+1/2) / exp(2*n+5/2). - Vaclav Kotesovec, May 09 2014

A247158 Number of binary n X n matrices in which each row or column sum is at most n/2.

Original entry on oeis.org

1, 1, 7, 34, 7343, 304186, 1709852332, 702998475376, 94473463102448047, 417235486592360297626, 1273060578884483984898786092, 63478599188626680785194983697744, 4243780803142765740205701619107014789924

Offset: 0

R. J. Mathar, Nov 21 2014

nonn

			a(2)=7 counts the following 2 X 2 matrices: 1 matrix with all zeros, 4 matrices where a 1 is at any of the four corners, and 2 matrices with 1's covering a diagonal.

Andrew Howroyd, Table of n, a(n) for n = 0..15
R. J. Mathar, The number of binary nXm matrices with at most k 1's in each row or column
E. Ordentlich, F. Parvaresh, R. M. Roth, Asymptotic enumeration of binary matrices with bounded row and column sums, SIAM J. Discrete Math. 26 (4) (2012) 1550-1575.
E. Ordentlich, F. Parvaresh, R. M. Roth, Asymptotic enumeration of binary matrices with bounded row and column weights, HPL-2011-239.

Cf. A197458, A283500.

a(6)-a(9) from Hiroaki Yamanouchi, Nov 22 2014
a(10)-a(11) from Hiroaki Yamanouchi, Nov 26 2014
a(12) from Andrew Howroyd, May 31 2017

A279445 Triangle read by rows: T(n, k) is the number of ways to place k points on an n X n square grid so that no more than 2 points are on a vertical or horizontal straight line.

Original entry on oeis.org

1, 1, 1, 4, 6, 4, 1, 1, 9, 36, 78, 90, 45, 6, 1, 16, 120, 528, 1428, 2304, 2040, 816, 90, 1, 25, 300, 2200, 10600, 34020, 71400, 93000, 67950, 22650, 2040, 1, 36, 630, 6900, 51525, 270720, 1005720, 2602800, 4531950, 4987800, 3110940, 888840, 67950, 1, 49, 1176, 17934

Offset: 1

Heinrich Ludwig, Dec 17 2016

Length of n-th row is A272651(n) + 1, where A272651(n) is the maximal number of points to be placed under the condition mentioned.
Rotations and reflections of placements are counted. If they are to be ignored, see A279453.
For condition "no more than 2 points on a straight line at any angle", see A194193 (but that one is read by antidiagonals).

			The table begins with T(1, 0):
1  1
1  4   6    4     1
1  9  36   78    90    45     6
1 16 120  528  1428  2304  2040   816    90
1 25 300 2200 10600 34020 71400 93000 67950 22650 2040
...
T(3, 2) = 36 because there are 36 ways to place 2 points on a 3 X 3 square grid so that no more than 2 points are on a vertical or horizontal straight line.

Heinrich Ludwig, Table of n, a(n) for n = 1..109

Row sums give A197458.
Columns 2..10: A000290, A083374, A279437, A279438, A279439, A279440, A279441, A279442, A279443.
Diagonal T(n, n) is A279444.
Cf. A279453, A194193.

A279437 Number of ways to place 3 points on an n X n square grid so that no more than 2 points are on a vertical or horizontal straight line.

Original entry on oeis.org

0, 4, 78, 528, 2200, 6900, 17934, 40768, 83808, 159300, 284350, 482064, 782808, 1225588, 1859550, 2745600, 3958144, 5586948, 7739118, 10541200, 14141400, 18711924, 24451438, 31587648, 40380000, 51122500, 64146654, 79824528, 98571928, 120851700, 147177150, 178115584

Offset: 1

Heinrich Ludwig, Dec 12 2016

Column 4 of triangle A279445.
Rotations and reflections of placements are counted. For numbers if they are to be ignored see A279447.
For condition "no more than 2 points on straight lines at any angle", see A045996.

Heinrich Ludwig, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Cf. A045996, A249447, A279444, A279445, A197458.

Same problem but 2, 4..9 points: A083374, A279438, A279439, A279440, A279441, A279442, A279443.

Table[(n^6 - 5 n^4 + 6 n^3 - 2 n^2)/6, {n, 32}] (* or *)
Rest@ CoefficientList[Series[2 x^2*(2 + 25 x + 33 x^2 + x^3 - x^4)/(1 - x)^7, {x, 0, 32}], x] (* Michael De Vlieger, Dec 12 2016 *)

concat(0, Vec(2*x^2*(2 + 25*x + 33*x^2 + x^3 - x^4) / (1 - x)^7 + O(x^50))) \\ Colin Barker, Dec 12 2016

a(n) = (n^6 - 5*n^4 + 6*n^3 - 2*n^2)/6.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7).
G.f.: 2*x^2*(2 + 25*x + 33*x^2 + x^3 - x^4) / (1 - x)^7. - Colin Barker, Dec 12 2016

A279438 Number of ways to place 4 points on an n X n square grid so that no more than 2 points are on a vertical or horizontal straight line.

Original entry on oeis.org

0, 1, 90, 1428, 10600, 51525, 190806, 584080, 1552608, 3701025, 8088850, 16470036, 31616520, 57743413, 101055150, 170433600, 278290816, 441610785, 683206218, 1033218100, 1530887400, 2226630021, 3184447750, 4484709648, 6227340000, 8535450625, 11559457026, 15481719540

Offset: 1

Heinrich Ludwig, Dec 12 2016

Column 5 of triangle A279445.
Rotations and reflections of placements are counted. For numbers if they are to be ignored see A279448.
For condition "no more than 2 points on straight lines at any angle", see A175383.

Heinrich Ludwig, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Cf. A175383, A249448, A279444, A279445, A197458.

Same problem but 2,3,5..9 points: A083374, A279437, A279439, A279440, A279441, A279442, A279443.

Table[(n^8 - 14 n^6 + 30 n^5 - 17 n^4 - 6 n^3 + 6 n^2)/24, {n, 28}] (* Michael De Vlieger, Dec 12 2016 *)
LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{0,1,90,1428,10600,51525,190806,584080,1552608},30] (* Harvey P. Dale, Sep 05 2024 *)

concat(0, Vec(x^2*(1 + 81*x + 654*x^2 + 904*x^3 + 99*x^4 - 57*x^5 - 2*x^6) / (1 - x)^9 + O(x^30))) \\ Colin Barker, Dec 13 2016

a(n) = (n^6 - 14*n^4 + 30*n^3 - 17*n^2 - 6*n + 6)*n^2/24 \\ Charles R Greathouse IV, Dec 13 2016

a(n) = (n^8 - 14*n^6 + 30*n^5 - 17*n^4 - 6*n^3 + 6*n^2)/24.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9).
G.f.: x^2*(1 + 81*x + 654*x^2 + 904*x^3 + 99*x^4 - 57*x^5 - 2*x^6) / (1 - x)^9. - Colin Barker, Dec 13 2016

A279439 Number of ways to place 5 points on an n X n square grid so that no more than 2 points are on a vertical or horizontal straight line.

Original entry on oeis.org

0, 0, 45, 2304, 34020, 270720, 1475145, 6209280, 21654864, 65422080, 176467005, 434206080, 990140580, 2117816064, 4288771305, 8284308480, 15355471680, 27446584320, 47501098029, 79872376320, 130866406020, 209448328320, 328150139625, 504222960384, 761083938000

Offset: 1

Heinrich Ludwig, Dec 21 2016

Column 6 of triangle A279445.
Rotations and reflections of placements are counted. For numbers if they are to be ignored see A279449.
For condition "no more than 2 points on straight lines at any angle", see A194190.

Heinrich Ludwig, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Cf. A194190, A279449, A279444, A279445, A197458.

Same problem but 2,3,4,6..9 points: A083374, A279437, A279438, A279440, A279441, A279442, A279443.

Table[(n^10 - 30 n^8 + 90 n^7 - 27 n^6 - 270 n^5 + 500 n^4 - 360 n^3 + 96 n^2)/120, {n, 25}] (* or *)
Rest@ CoefficientList[Series[9 x^3*(5 + 201 x + 1239 x^2 + 1755 x^3 + 335 x^4 - 165 x^5 - 11 x^6 + x^7)/(1 - x)^11, {x, 0, 25}], x] (* Michael De Vlieger, Dec 22 2016 *)

concat(vector(2), Vec(9*x^3*(5 +201*x +1239*x^2 +1755*x^3 +335*x^4 -165*x^5 -11*x^6 +x^7) / (1 -x)^11 + O(x^30))) \\ Colin Barker, Dec 22 2016

a(n) = (n^10 -30*n^8 +90*n^7 -27*n^6 -270*n^5 +500*n^4 -360*n^3 +96*n^2)/120.
a(n) = 11*a(n-1) -55*a(n-2) +165*a(n-3) -330*a(n-4) +462*a(n-5) -462*a(n-6) +330*a(n-7) -165*a(n-8) +55*a(n-9) -11*a(n-10) +*a(n-11).
G.f.: 9*x^3*(5 +201*x +1239*x^2 +1755*x^3 +335*x^4 -165*x^5 -11*x^6 +x^7) / (1 -x)^11. - Colin Barker, Dec 22 2016

A279440 Number of ways to place 6 points on an n X n square grid so that no more than 2 points are on a vertical or horizontal straight line.

Original entry on oeis.org

0, 0, 6, 2040, 71400, 1005720, 8421630, 50092896, 233483040, 905925600, 3045791430, 9125544120, 24868110696, 62593429080, 147255640350, 326843422080, 689604309120, 1391614736256, 2699616160710, 5055848825400, 9173923662120, 16177675640280, 27798546316926, 46651469520480

Offset: 1

Heinrich Ludwig, Dec 22 2016

Column 7 of triangle A279445.
Rotations and reflections of placements are counted. For numbers if they are to be ignored see A279450.
For condition "no more than 2 points on straight lines at any angle", see A194191.

Heinrich Ludwig, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

Cf. A194191, A279450, A279444, A279445, A197458.

Same problem but 2..5,7,8,9 points: A083374, A279437, A279438, A279439, A279441, A279442, A279443.

Table[(n^12 - 55 n^10 + 210 n^9 + 93 n^8 - 2220 n^7 + 5855 n^6 - 7350 n^5 + 4786 n^4 - 1440 n^3 + 120 n^2)/720, {n, 24}] (* or *)
Rest@ CoefficientList[Series[6 x^3 (1 + 327 x + 7558 x^2 + 39154 x^3 + 56220 x^4 + 14724 x^5 - 6262 x^6 - 978 x^7 + 131 x^8 + 5 x^9)/(1 - x)^13, {x, 0, 24}], x] (* Michael De Vlieger, Dec 22 2016 *)

concat(vector(2), Vec(6*x^3*(1 +327*x +7558*x^2 +39154*x^3 +56220*x^4 +14724*x^5 -6262*x^6 -978*x^7 +131*x^8 +5*x^9) / (1 -x)^13 + O(x^30))) \\ Colin Barker, Dec 22 2016

a(n) = (n^12 -55*n^10 +210*n^9 +93*n^8 -2220*n^7 +5855*n^6 -7350*n^5 +4786*n^4 -1440*n^3 +120*n^2)/720.
a(n) = 13*a(n-1) -78*a(n-2) +286*a(n-3) -715*a(n-4) +1287*a(n-5) -1716*a(n-6) +1716*a(n-7) -1287*a(n-8) +715*a(n-9) -286*a(n-10) +78*a(n-11) -13*a(n-12) +*a(n-13).
G.f.: 6*x^3*(1 +327*x +7558*x^2 +39154*x^3 +56220*x^4 +14724*x^5 -6262*x^6 -978*x^7 +131*x^8 +5*x^9) / (1 -x)^13. - Colin Barker, Dec 22 2016

A279441 Number of ways to place 7 points on an n X n square grid so that no more than 2 points are on a vertical or horizontal straight line.

Original entry on oeis.org

0, 0, 0, 816, 93000, 2602800, 35526120, 309328320, 1972234656, 9989784000, 42369069600, 155993500080, 511660972680, 1524225598896, 4185197289000, 10715254368000, 25817751281280, 58981960615680, 128554066935936, 268691201838000, 540886175310600, 1052558059827120

Offset: 1

Heinrich Ludwig, Dec 22 2016

Column 8 of triangle A279445.
Rotations and reflections of placements are counted. For numbers if they are to be ignored see A279451.
For condition "no more than 2 points on straight lines at any angle", see A194192.

Heinrich Ludwig, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (15,-105,455,-1365,3003,-5005,6435,-6435,5005,-3003,1365,-455,105,-15,1).

Cf. A194192, A279451, A279444, A279445, A197458.

Same problem but 2..6,8,9 points: A083374, A279437, A279438, A279439, A279440, A279442, A279443.

Table[(n^14 - 91 n^12 + 420 n^11 + 693 n^10 - 10500 n^9 + 33647 n^8 - 45780 n^7 + 5866 n^6 + 65940 n^5 - 89796 n^4 + 50400 n^3 - 10800 n^2)/5040, {n, 23}] (* or *)
Rest@ CoefficientList[Series[24 x^4*(34 + 3365 x + 53895 x^2 + 244910 x^3 + 355390 x^4 + 115542 x^5 - 42490 x^6 - 11570 x^7 + 1500 x^8 + 145 x^9 - x^10)/(1 - x)^15, {x, 0, 23}], x] (* Michael De Vlieger, Dec 22 2016 *)

concat(vector(3), Vec(24*x^4*(34 +3365*x +53895*x^2 +244910*x^3 +355390*x^4 +115542*x^5 -42490*x^6 -11570*x^7 +1500*x^8 +145*x^9 -x^10) / (1 -x)^15 + O(x^30))) \\ Colin Barker, Dec 22 2016

a(n) = (n^12 -91*n^10 +420*n^9 +693*n^8 -10500*n^7 +33647*n^6 -45780*n^5 +5866*n^4 +65940*n^3 -89796*n^2 +50400*n -10800)*n^2/5040 \\ Charles R Greathouse IV, Dec 22 2016

a(n) = (n^14 -91*n^12 +420*n^11 +693*n^10 -10500*n^9 +33647*n^8 -45780*n^7 +5866*n^6 +65940*n^5 -89796*n^4 +50400*n^3 -10800*n^2)/5040.
a(n) = 15*a(n-1) -105*a(n-2) +455*a(n-3) -1365*a(n-4) +3003*a(n-5) -5005*a(n-6) +6435*a(n-7) -6435*a(n-8) +5005*a(n-9) -3003*a(n-10) +1365*a(n-11) -455*a(n-12) +105*a(n-13) -15*a(n-14) +a(n-15).
G.f.: 24*x^4*(34 +3365*x +53895*x^2 +244910*x^3 +355390*x^4 +115542*x^5 -42490*x^6 -11570*x^7 +1500*x^8 +145*x^9 -x^10) / (1 -x)^15. - Colin Barker, Dec 22 2016

A279442 Number of ways to place 8 points on an n X n square grid so that no more than 2 points are on a vertical or horizontal straight line.

Original entry on oeis.org

0, 0, 0, 90, 67950, 4531950, 109425330, 1460297160, 13112872920, 88456195800, 480149029800, 2196080372970, 8743233946590, 31033043111070, 99992483914050, 296626638016800, 819218054279520, 2125440234303840, 5218743585428640, 12201529135725450, 27304286810701950

Offset: 1

Heinrich Ludwig, Dec 22 2016

Column 9 of triangle A279445.

Rotations and reflections of placements are counted.

Heinrich Ludwig, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (17,-136,680,-2380,6188,-12376,19448,-24310,24310,-19448,12376,-6188,2380,-680,136,-17,1).

Cf. A279444, A279445, A197458.

Same problem but 2..7,9 points: A083374, A279437, A279438, A279439, A279440, A279441, A279443.

Table[n^2*(n - 1)^2*(n - 2)^2*(n - 3)^2*(n^8 + 12 n^7 - 54 n^6 - 444 n^5 + 1845 n^4 + 1392 n^3 - 11332 n^2 + 9660 n + 1260)/8!, {n, 21}] (* Michael De Vlieger, Dec 22 2016 *)

concat(vector(3), Vec(90*x^4*(1 +738*x +37656*x^2 +461802*x^3 +1893555*x^4 +2767824*x^5 +1058064*x^6 -331920*x^7 -140913*x^8 +15950*x^9 +3096*x^10 -90*x^11 -3*x^12) / (1 -x)^17 + O(x^30))) \\ Colin Barker, Dec 23 2016

a(n) = (n^16 -140*n^14 +756*n^13 +2506*n^12 -36540*n^11 +130940*n^10 -117432*n^9 -559615*n^8 +2186100*n^7 -3622360*n^6 +3228876*n^5 -1439892*n^4 +181440*n^3 +45360*n^2)/40320; factorized: a(n) = n^2*(n-1)^2*(n-2)^2*(n-3)^2*(n^8 +12*n^7 -54*n^6 -444*n^5 +1845*n^4 +1392*n^3 -11332*n^2 +9660*n +1260)/8!.
a(n) = SUM(1<=j<=17, C(17,j)*(-1)^(j-1)*a(n-j)).
G.f.: 90*x^4*(1 +738*x +37656*x^2 +461802*x^3 +1893555*x^4 +2767824*x^5 +1058064*x^6 -331920*x^7 -140913*x^8 +15950*x^9 +3096*x^10 -90*x^11 -3*x^12) / (1 -x)^17. - Colin Barker, Dec 23 2016

A279443 Number of ways to place 9 points on an n X n board so that no more than 2 points are on a vertical or horizontal straight line.

Original entry on oeis.org

0, 0, 0, 0, 22650, 4987800, 240023070, 5219088000, 68483325960, 630486309600, 4456523194200, 25647802519680, 125166919041450, 533442526857240, 2029603476250350, 7011735609715200, 22291042191643680, 65914292362262400, 182880685655641440, 479548000781222400

Offset: 1

Heinrich Ludwig, Dec 24 2016

Column 9 of triangle A279445.

Rotations and reflections of placements are counted.

Heinrich Ludwig, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (19,-171,969,-3876,11628, -27132,50388,-75582,92378,-92378,75582,-50388,27132,-11628,3876, -969,171,-19,1).

Cf. A279444, A279445, A197458.

Same problem but 2..8 points: A083374, A279437, A279438, A279439, A279440, A279441, A279442.

concat(vector(4), Vec(30*x^5*(755 +151915*x +4970934*x^2 +49653854*x^3 +187307071*x^4 +275138271*x^5 +119386656*x^6 -31251744*x^7 -19595619*x^8 +1706821*x^9 +667466*x^10 -26334*x^11 -2543*x^12 +17*x^13) / (1 -x)^19 + O(x^30))) \\ Colin Barker, Dec 24 2016

a(n) = (n^18 -204*n^16 +1260*n^15 +6846*n^14 -104076*n^13 +394504*n^12 +128520*n^11 -6237075*n^10 +24018372*n^9 -43820196*n^8 +30400020*n^7 +34251148*n^6 -99199296*n^5 +98504496*n^4 -47779200*n^3 +9434880*n^2)/362880; factorized: a(n) = n^2*(n-1)^2*(n-2)^2*(n-3)^2*(n-4)^2*(n^8 +20*n^7 +26*n^6 -820*n^5 -247*n^4 +9704*n^3 -9104*n^2 -14700*n +16380)/9!.
a(n) = SUM(1<=j<=19, C(19,j)*(-1)^(j-1)*a(n-j)).
G.f.: 30*x^5*(755 +151915*x +4970934*x^2 +49653854*x^3 +187307071*x^4 +275138271*x^5 +119386656*x^6 -31251744*x^7 -19595619*x^8 +1706821*x^9 +667466*x^10 -26334*x^11 -2543*x^12 +17*x^13) / (1 -x)^19. - Colin Barker, Dec 24 2016

cp's OEIS Frontend

A007107 Number of labeled 2-regular digraphs with n nodes.

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A247158 Number of binary n X n matrices in which each row or column sum is at most n/2.

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A279445 Triangle read by rows: T(n, k) is the number of ways to place k points on an n X n square grid so that no more than 2 points are on a vertical or horizontal straight line.

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A279437 Number of ways to place 3 points on an n X n square grid so that no more than 2 points are on a vertical or horizontal straight line.

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A279438 Number of ways to place 4 points on an n X n square grid so that no more than 2 points are on a vertical or horizontal straight line.

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A279439 Number of ways to place 5 points on an n X n square grid so that no more than 2 points are on a vertical or horizontal straight line.

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A279440 Number of ways to place 6 points on an n X n square grid so that no more than 2 points are on a vertical or horizontal straight line.

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A279441 Number of ways to place 7 points on an n X n square grid so that no more than 2 points are on a vertical or horizontal straight line.

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