A220935 -id:A220935 - cp's OEIS frontend

A220932 Equals two maps: number of n X 3 binary arrays indicating the locations of corresponding elements equal to exactly two of their horizontal and antidiagonal neighbors in a random 0..2 n X 3 array.

2, 16, 92, 556, 3332, 19996, 119972, 719836, 4319012, 25914076, 155484452, 932906716, 5597440292, 33584641756, 201507850532, 1209047103196, 7254282619172, 43525695715036, 261154174290212, 1566925045741276

Offset: 1

R. H. Hardin, Dec 25 2012

nonn

Column 3 of A220935.

			Some solutions for n=3:
..0..1..0....0..1..1....0..1..0....0..0..0....0..0..0....0..1..0....0..0..0
..0..0..1....1..0..1....0..1..0....1..0..1....0..0..1....0..0..0....0..1..0
..1..1..0....1..0..0....0..1..0....1..0..0....0..1..0....1..1..0....1..0..0

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A220935.

Empirical: a(n) = 5*a(n-1) + 6*a(n-2).
Conjectures from Colin Barker, Mar 13 2018: (Start)
G.f.: 2*x*(1 + 3*x) / ((1 + x)*(1 - 6*x)).
a(n) = (2^n*3^(n+1) + 4) / 7 for n even.
a(n) = (2^n*3^(n+1) - 4) / 7 for n odd
(End)

A220933 Equals two maps: number of nX4 binary arrays indicating the locations of corresponding elements equal to exactly two of their horizontal and antidiagonal neighbors in a random 0..2 nX4 array.

Original entry on oeis.org

4, 52, 673, 9107, 123958, 1686304, 22931365, 311813067, 4239917031, 57652874111, 783943412638, 10659785895199, 144948006719997, 1970951840091756, 26800307525626867, 364421123267042408, 4955269821323438717

Offset: 1

R. H. Hardin Dec 25 2012

nonn

Column 4 of A220935

			Some solutions for n=3
..0..0..0..0....0..0..1..0....0..1..0..0....0..1..1..0....0..1..1..0
..0..0..0..0....0..0..0..0....1..0..0..1....0..0..0..1....0..0..1..0
..0..0..0..0....0..0..1..0....1..0..1..0....1..0..1..0....0..0..1..0

R. H. Hardin, Table of n, a(n) for n = 1..156

Empirical: a(n) = 28*a(n-1) -296*a(n-2) +1804*a(n-3) -7384*a(n-4) +21847*a(n-5) -48816*a(n-6) +85558*a(n-7) -123954*a(n-8) +160701*a(n-9) -200185*a(n-10) +236867*a(n-11) -248056*a(n-12) +226758*a(n-13) -197374*a(n-14) +171224*a(n-15) -136118*a(n-16) +103073*a(n-17) -90758*a(n-18) +83397*a(n-19) -61987*a(n-20) +38070*a(n-21) -26150*a(n-22) +15689*a(n-23) -3389*a(n-24) -92*a(n-25) -312*a(n-26) +112*a(n-27) -16*a(n-28)

A220936 Equals two maps: number of 2Xn binary arrays indicating the locations of corresponding elements equal to exactly two of their horizontal and antidiagonal neighbors in a random 0..2 2Xn array.

Original entry on oeis.org

1, 4, 16, 52, 200, 792, 3080, 12164, 47827, 188078, 739654, 2908308, 11433623, 44951623, 176719636, 694738324, 2731215010, 10737125607, 42210368413, 165939449883, 652348443363, 2564539277676, 10081819289214, 39634040551712

Offset: 1

R. H. Hardin Dec 25 2012

nonn

Row 2 of A220935

			Some solutions for n=3
..0..0..1....0..0..0....0..1..0....0..1..0....0..0..1....0..0..1....0..1..1
..0..0..0....1..0..0....1..1..0....1..0..0....0..1..0....1..1..0....1..0..0

R. H. Hardin, Table of n, a(n) for n = 1..210

Empirical: a(n) = 8*a(n-1) -22*a(n-2) +36*a(n-3) -83*a(n-4) +180*a(n-5) -202*a(n-6) +134*a(n-7) -163*a(n-8) -148*a(n-9) +1102*a(n-10) -1964*a(n-11) +2361*a(n-12) -2806*a(n-13) +1954*a(n-14) +698*a(n-15) -6089*a(n-16) +12746*a(n-17) -16274*a(n-18) +16250*a(n-19) -15958*a(n-20) +11458*a(n-21) +1206*a(n-22) -9876*a(n-23) +17244*a(n-24) -3208*a(n-25) +14772*a(n-26) -4156*a(n-27) +26925*a(n-28) +6308*a(n-29) +50808*a(n-30) +12984*a(n-31) +97889*a(n-32) +17770*a(n-33) +128262*a(n-34) +38432*a(n-35) +149644*a(n-36) +109876*a(n-37) +157919*a(n-38) +178940*a(n-39) +130160*a(n-40) +199080*a(n-41) +94482*a(n-42) +171386*a(n-43) +61079*a(n-44) +118320*a(n-45) +49065*a(n-46) +54958*a(n-47) +32068*a(n-48) +15960*a(n-49) +13770*a(n-50) +6182*a(n-51) +4376*a(n-52) +1600*a(n-53) +766*a(n-54) +188*a(n-55) +28*a(n-56) -8*a(n-57)

A220934 Equals two maps: number of nX5 binary arrays indicating the locations of corresponding elements equal to exactly two of their horizontal and antidiagonal neighbors in a random 0..2 nX5 array.

Original entry on oeis.org

7, 200, 5912, 172904, 4983202, 143495572, 4129000493, 118791182035, 3417440488681, 98313052773312, 2828261800424005, 81363108971612428, 2340643785326878730, 67335342944117783361, 1937094540263542667587

Offset: 1

R. H. Hardin Dec 25 2012

nonn

Column 5 of A220935

			Some solutions for n=3
..0..1..0..1..1....0..0..1..0..0....0..1..1..0..0....0..0..0..0..1
..0..0..0..0..1....1..1..1..0..0....1..0..0..0..0....0..1..0..0..1
..0..1..1..1..0....0..0..1..1..0....0..0..0..1..0....0..0..0..1..0

R. H. Hardin, Table of n, a(n) for n = 1..16

A220937 Equals two maps: number of 3Xn binary arrays indicating the locations of corresponding elements equal to exactly two of their horizontal and antidiagonal neighbors in a random 0..2 3Xn array.

Original entry on oeis.org

1, 12, 92, 673, 5912, 48212, 395844, 3232729, 26184472, 211363254

Offset: 1

R. H. Hardin Dec 25 2012

nonn

Row 3 of A220935

			Some solutions for n=3
..0..0..1....0..0..1....0..0..1....0..1..1....0..1..1....0..0..0....0..1..0
..0..0..1....1..0..0....1..0..1....0..1..1....0..0..0....0..1..0....1..0..0
..1..1..0....0..1..0....0..0..0....0..0..0....0..0..0....0..1..0....0..1..0

A220938 Equals two maps: number of 4Xn binary arrays indicating the locations of corresponding elements equal to exactly two of their horizontal and antidiagonal neighbors in a random 0..2 4Xn array.

Original entry on oeis.org

1, 37, 556, 9107, 172904, 2876430, 49406891

Offset: 1

R. H. Hardin Dec 25 2012

nonn

Row 4 of A220935

			Some solutions for n=3
..0..0..1....0..0..0....0..0..0....0..0..1....0..0..1....0..1..0....0..1..1
..0..1..1....0..0..0....0..0..0....1..1..0....1..0..1....1..0..0....0..0..0
..0..0..1....0..1..0....0..1..0....0..1..1....1..0..0....0..1..1....0..1..1
..1..1..0....0..1..0....1..1..0....0..0..0....0..1..0....1..1..0....0..0..0

cp's OEIS Frontend

A220932 Equals two maps: number of n X 3 binary arrays indicating the locations of corresponding elements equal to exactly two of their horizontal and antidiagonal neighbors in a random 0..2 n X 3 array.

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A220933 Equals two maps: number of nX4 binary arrays indicating the locations of corresponding elements equal to exactly two of their horizontal and antidiagonal neighbors in a random 0..2 nX4 array.

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A220936 Equals two maps: number of 2Xn binary arrays indicating the locations of corresponding elements equal to exactly two of their horizontal and antidiagonal neighbors in a random 0..2 2Xn array.

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A220934 Equals two maps: number of nX5 binary arrays indicating the locations of corresponding elements equal to exactly two of their horizontal and antidiagonal neighbors in a random 0..2 nX5 array.

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A220937 Equals two maps: number of 3Xn binary arrays indicating the locations of corresponding elements equal to exactly two of their horizontal and antidiagonal neighbors in a random 0..2 3Xn array.

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A220938 Equals two maps: number of 4Xn binary arrays indicating the locations of corresponding elements equal to exactly two of their horizontal and antidiagonal neighbors in a random 0..2 4Xn array.

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