A196146 -id:A196146 - cp's OEIS frontend

A196140 Number of nX2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,4,1,2 for x=0,1,2,3,4.

3, 5, 8, 17, 34, 62, 123, 243, 471, 924, 1817, 3558, 6978, 13697, 26865, 52699, 103398, 202847, 397944, 780720, 1531657, 3004865, 5895113, 11565346, 22689467, 44513380, 87328672, 171325871, 336115955, 659409701, 1293664016, 2537976953, 4979134498

Offset: 1

R. H. Hardin Sep 28 2011

nonn

Every 0 is next to 0 3's, every 1 is next to 1 0's, every 2 is next to 2 4's, every 3 is next to 3 1's, every 4 is next to 4 2's

Column 2 of A196146

			Some solutions for n=4
.1.0...0.1...1.0...0.0...0.1...1.0...1.0...1.0...0.0...1.1
.1.0...1.3...3.1...0.0...0.1...1.1...1.0...3.1...1.1...0.0
.1.1...3.1...1.1...0.0...1.1...0.1...1.0...1.3...1.1...0.0
.0.1...1.0...0.0...1.1...1.0...0.1...1.0...0.1...0.0...0.0

R. H. Hardin, Table of n, a(n) for n = 1..200

Empirical: a(n) = 2*a(n-1) +a(n-3) -2*a(n-4) -a(n-5) +a(n-6)

A196141 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,4,1,2 for x=0,1,2,3,4.

Original entry on oeis.org

4, 8, 7, 26, 49, 85, 178, 348, 683, 1349, 2688, 5319, 10498, 20818, 41206, 81574, 161646, 320215, 634294, 1256481, 2489029, 4930656, 9767642, 19350237, 38333645, 75940498, 150441579, 298031468, 590414638, 1169642000, 2317123308, 4590345948

Offset: 1

R. H. Hardin, Sep 28 2011

nonn

Every 0 is next to 0 3's, every 1 is next to 1 0's, every 2 is next to 2 4's, every 3 is next to 3 1's, every 4 is next to 4 2's.

Column 3 of A196146.

			Some solutions for n=4:
.0.1.1...1.1.0...0.0.0...1.0.0...1.0.1...0.0.1...0.0.1
.1.1.0...0.1.1...1.1.1...3.1.1...1.0.1...0.0.1...1.1.1
.3.1.1...1.1.3...1.1.3...1.1.1...1.0.1...0.0.1...1.1.0
.1.0.1...1.0.1...0.0.1...0.0.0...1.0.1...0.0.1...0.1.1

R. H. Hardin, Table of n, a(n) for n = 1..200
Robert Israel, Maple-assisted proof of empirical recurrence

Cf. A196146.

Empirical: a(n) = 3*a(n-1) -2*a(n-2) +a(n-3) -3*a(n-4) +3*a(n-5) -a(n-6) -7*a(n-8) +a(n-9) +4*a(n-10) +2*a(n-11) +6*a(n-12).
Empirical g.f.: x*(4 - 4*x - 9*x^2 + 17*x^3 - 11*x^4 - 5*x^5 - 4*x^6 + 14*x^8 + 4*x^9 + 12*x^10) / (1 - 3*x + 2*x^2 - x^3 + 3*x^4 - 3*x^5 + x^6 + 7*x^8 - x^9 - 4*x^10 - 2*x^11 - 6*x^12). - Colin Barker, May 08 2018
Empirical formulas verified: see link. - Robert Israel, Jan 21 2019

A196143 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,4,1,2 for x=0,1,2,3,4.

Original entry on oeis.org

8, 34, 49, 168, 481, 1031, 2781, 7666, 19581, 50767, 133067, 347285, 908050, 2376097, 6205040, 16210548, 42388933, 110845205, 289736000, 757344081, 1979883152, 5176072691, 13531879986, 35376145849, 92481993251, 241773334844

Offset: 1

R. H. Hardin Sep 28 2011

nonn

Every 0 is next to 0 3's, every 1 is next to 1 0's, every 2 is next to 2 4's, every 3 is next to 3 1's, every 4 is next to 4 2's

Column 5 of A196146

			Some solutions for n=4
.1.0.0.0.0...0.1.1.0.1...1.0.1.1.1...1.1.1.1.1
.3.1.1.1.1...0.1.1.0.1...3.1.1.0.0...0.0.0.0.0
.1.3.3.1.3...0.1.1.0.1...1.1.1.0.0...0.0.0.0.0
.0.1.1.0.1...0.1.1.0.1...0.0.1.1.1...1.1.1.1.1

R. H. Hardin, Table of n, a(n) for n = 1..200

Empirical: a(n) = 5*a(n-1) -9*a(n-2) +12*a(n-3) -14*a(n-4) +5*a(n-5) +10*a(n-6) -69*a(n-7) +129*a(n-8) -145*a(n-9) +164*a(n-10) -196*a(n-11) +218*a(n-12) +394*a(n-13) -349*a(n-14) +295*a(n-15) -1023*a(n-16) +924*a(n-17) -298*a(n-18) +1097*a(n-19) -4595*a(n-20) -2208*a(n-21) +627*a(n-22) +2723*a(n-23) -690*a(n-24) -19588*a(n-25) +6132*a(n-26) +2659*a(n-27) +23034*a(n-28) +3305*a(n-29) +847*a(n-30) +42867*a(n-31) +37263*a(n-32) +85485*a(n-33) +47600*a(n-34) +98716*a(n-35) +83847*a(n-36) +39595*a(n-37) -5290*a(n-38) -194971*a(n-39) -247776*a(n-40) -380416*a(n-41) -386837*a(n-42) -332348*a(n-43) -375756*a(n-44) -286048*a(n-45) -312418*a(n-46) -286684*a(n-47) -274384*a(n-48) -251047*a(n-49) -167220*a(n-50) -126756*a(n-51) -65057*a(n-52) -32030*a(n-53) -7322*a(n-54) -100*a(n-55) +2812*a(n-56) +408*a(n-57) +568*a(n-58) -264*a(n-59) +32*a(n-61)

A196144 Number of nX6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,4,1,2 for x=0,1,2,3,4.

Original entry on oeis.org

12, 62, 85, 346, 1031, 2599, 7486, 22292, 61689, 177057, 510032, 1448637, 4132242, 11862868, 33916712, 96889032, 277372934, 794009775, 2271276412, 6499360165, 18601549495, 53231495224, 152336019308, 435981877255, 1247751132201

Offset: 1

R. H. Hardin Sep 28 2011

nonn

Every 0 is next to 0 3's, every 1 is next to 1 0's, every 2 is next to 2 4's, every 3 is next to 3 1's, every 4 is next to 4 2's

Column 6 of A196146

			Some solutions for n=4
.1.1.3.1.0.0...1.1.0.0.0.0...0.0.1.1.0.0...0.0.0.0.0.1
.0.0.1.1.0.0...0.1.1.1.1.1...1.1.3.3.1.1...1.1.1.1.1.1
.0.0.1.1.0.0...1.1.1.1.1.1...3.1.1.1.1.1...3.1.1.1.1.0
.0.0.1.3.1.1...1.0.0.0.0.0...1.0.0.0.0.0...1.0.0.0.1.1

R. H. Hardin, Table of n, a(n) for n = 1..200

A196145 Number of nX7 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,4,1,2 for x=0,1,2,3,4.

Original entry on oeis.org

17, 123, 178, 865, 2781, 7486, 24615, 85533, 266059, 866323, 2817802, 9024682, 29161693, 94823673, 306912929, 992919095, 3216924395, 10417479713, 33734415945, 109304966265, 354134153161, 1147139951832, 3716343382506

Offset: 1

R. H. Hardin Sep 28 2011

nonn

Every 0 is next to 0 3's, every 1 is next to 1 0's, every 2 is next to 2 4's, every 3 is next to 3 1's, every 4 is next to 4 2's

Column 7 of A196146

			Some solutions for n=4
.1.0.0.1.1.0.0...1.3.1.0.0.0.1...1.0.0.1.1.0.1
.3.1.1.1.1.1.1...0.1.1.0.0.0.1...3.1.1.3.3.1.1
.1.1.1.0.0.1.1...0.1.1.1.1.1.1...1.1.1.1.1.1.0
.0.0.1.1.1.1.0...1.1.0.1.3.1.0...0.0.0.0.0.1.1

R. H. Hardin, Table of n, a(n) for n = 1..200

A196139 Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,0,4,1,2 for x=0,1,2,3,4.

Original entry on oeis.org

1, 5, 7, 83, 481, 2599, 24615, 330889, 4431097, 82611569, 1973678929, 55783136985

Offset: 1

R. H. Hardin Sep 28 2011

nonn

Every 0 is next to 0 3's, every 1 is next to 1 0's, every 2 is next to 2 4's, every 3 is next to 3 1's, every 4 is next to 4 2's

Diagonal of A196146

			Some solutions for n=4
.1.3.1.0...0.1.3.1...1.3.1.0...0.0.1.1...0.1.1.0
.0.1.1.0...0.1.1.0...0.1.1.0...1.1.1.0...1.1.1.1
.1.1.1.1...0.1.1.0...0.1.1.1...3.1.1.0...1.0.0.1
.1.0.0.1...1.3.1.0...1.1.0.1...1.0.1.1...1.0.0.1

A196142 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,4,1,2 for x=0,1,2,3,4.

Original entry on oeis.org

5, 17, 26, 83, 168, 346, 865, 2055, 4745, 10866, 24967, 57786, 134514, 312597, 722915, 1670991, 3869674, 8969607, 20789120, 48159310, 111529135, 258315343, 598428365, 1386426078, 3211799633, 7440009880, 17234511484, 39924363651, 92487922123

Offset: 1

R. H. Hardin Sep 28 2011

nonn

Every 0 is next to 0 3's, every 1 is next to 1 0's, every 2 is next to 2 4's, every 3 is next to 3 1's, every 4 is next to 4 2's

Column 4 of A196146

			Some solutions for n=5
.0.1.3.1...0.1.1.0...0.1.3.1...1.0.0.1...0.0.0.1
.0.1.1.0...1.1.1.1...0.1.1.0...1.1.1.1...0.0.0.1
.1.3.1.0...1.0.0.1...1.3.3.1...0.1.1.0...1.1.1.3
.1.3.1.0...1.1.1.1...3.1.1.1...0.1.1.0...1.1.1.1
.0.1.3.1...0.1.1.0...1.0.0.0...1.3.1.0...0.0.0.0

Empirical: a(n) = 5*a(n-1) -9*a(n-2) +9*a(n-3) -8*a(n-4) +12*a(n-5) -20*a(n-6) -a(n-7) +21*a(n-8) +5*a(n-9) -11*a(n-10) -60*a(n-11) +128*a(n-12) +17*a(n-13) -20*a(n-14) -77*a(n-15) +15*a(n-16) -15*a(n-17) -28*a(n-18) -32*a(n-19) -118*a(n-20) +28*a(n-21) -65*a(n-22) -17*a(n-23) -22*a(n-24) +12*a(n-25) -15*a(n-26) +3*a(n-28)

cp's OEIS Frontend

A196140 Number of nX2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,4,1,2 for x=0,1,2,3,4.

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A196141 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,4,1,2 for x=0,1,2,3,4.

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A196143 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,4,1,2 for x=0,1,2,3,4.

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A196144 Number of nX6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,4,1,2 for x=0,1,2,3,4.

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A196145 Number of nX7 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,4,1,2 for x=0,1,2,3,4.

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A196139 Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 3,0,4,1,2 for x=0,1,2,3,4.

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A196142 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,4,1,2 for x=0,1,2,3,4.

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