cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-7 of 7 results.

A196132 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,3,4 for x=0,1,2,3,4.

Original entry on oeis.org

0, 4, 3, 8, 14, 19, 46, 56, 133, 184, 372, 599, 1064, 1874, 3147, 5692, 9516, 17053, 28980, 51004, 88089, 153086, 266660, 461205, 804810, 1392380, 2426083, 4205680, 7313450, 12699273, 22056242, 38328650, 66544359, 115648570, 200804584
Offset: 1

Views

Author

R. H. Hardin, Sep 28 2011

Keywords

Comments

Every 0 is next to 0 0's, every 1 is next to 1 2's, every 2 is next to 2 1's, every 3 is next to 3 3's, every 4 is next to 4 4's.
Column 2 of A196138.

Examples

			All solutions for n=4:
..0..1....2..1....1..2....2..1....1..0....0..1....1..0....1..2
..1..2....1..0....0..1....1..0....2..1....1..2....2..1....0..1
..1..0....0..1....2..1....1..2....0..1....1..2....2..1....1..0
..2..1....1..2....1..0....0..1....1..2....0..1....1..0....2..1
		

Crossrefs

Cf. A196138.

Formula

Empirical: a(n) = 3*a(n-2) +2*a(n-3) -2*a(n-4) -3*a(n-5) -a(n-6) +4*a(n-7) -2*a(n-9).
Empirical g.f.: x^2*(4 + 3*x - 4*x^2 - 3*x^3 - 3*x^4 + 6*x^5 - 4*x^7) / ((1 - x)*(1 + x - 2*x^2 - 4*x^3 - 2*x^4 + x^5 + 2*x^6 - 2*x^7 - 2*x^8)). - Colin Barker, May 08 2018

A196133 Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,3,4 for x=0,1,2,3,4.

Original entry on oeis.org

1, 3, 4, 19, 31, 70, 117, 253, 538, 1169, 2401, 4896, 10179, 21291, 44754, 93367, 194747, 405806, 848007, 1772209, 3704016, 7737207, 16162351, 33766226, 70554991, 147429719, 308053298, 643669403, 1344939023, 2810299720, 5872263661
Offset: 1

Views

Author

R. H. Hardin Sep 28 2011

Keywords

Comments

Every 0 is next to 0 0's, every 1 is next to 1 2's, every 2 is next to 2 1's, every 3 is next to 3 3's, every 4 is next to 4 4's
Column 3 of A196138

Examples

			Some solutions for n=4
..1..1..2....0..1..2....1..1..2....1..2..1....0..1..2....2..1..1....0..1..2
..2..1..1....2..1..1....2..0..1....1..2..1....1..0..1....1..1..2....1..0..1
..2..1..1....1..1..0....1..1..0....1..2..1....2..1..1....1..1..2....2..2..1
..1..1..2....0..2..1....0..2..1....1..2..1....0..1..2....2..1..1....1..1..0
		

Formula

Empirical: a(n) = a(n-1) +a(n-2) +a(n-3) +3*a(n-4) +3*a(n-5) +6*a(n-6) -5*a(n-7) -14*a(n-8) -17*a(n-9) -32*a(n-10) -25*a(n-11) -38*a(n-12) -11*a(n-13) +19*a(n-14) +39*a(n-15) +42*a(n-16) +6*a(n-17) +18*a(n-18) +20*a(n-19) +32*a(n-20) +24*a(n-21)

A196134 Number of n X 4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,3,4 for x=0,1,2,3,4.

Original entry on oeis.org

2, 8, 19, 31, 165, 251, 931, 1880, 5556, 15236, 36242, 100659, 238001, 672366, 1720580, 4457811, 11495347, 29435188, 78700799, 203112497, 528285928, 1357620133, 3537680945, 9273276601, 24073315272, 62428922801, 161432508844
Offset: 1

Views

Author

R. H. Hardin, Sep 28 2011

Keywords

Comments

Every 0 is next to 0 0's, every 1 is next to 1 2's, every 2 is next to 2 1's, every 3 is next to 3 3's, every 4 is next to 4 4's.
Column 4 of A196138.

Examples

			Some solutions for n=5
..1..2..2..1....0..1..1..1....1..2..2..1....2..1..0..1....0..1..1..0
..0..1..1..0....1..2..2..2....1..1..1..0....1..1..2..2....1..2..2..1
..2..1..1..2....1..0..1..1....2..0..1..2....1..1..1..1....1..2..2..1
..1..1..1..1....2..2..1..1....1..1..1..1....2..2..0..1....1..1..1..1
..1..2..2..1....1..1..1..2....1..2..2..1....1..1..1..2....2..1..1..2
		

Crossrefs

Cf. A196138.

Formula

Empirical: a(n) = 3*a(n-2) +8*a(n-3) +a(n-4) +39*a(n-5) +4*a(n-6) -158*a(n-7) -388*a(n-8) +591*a(n-9) +760*a(n-10) -736*a(n-11) -3520*a(n-12) +2311*a(n-13) +3825*a(n-14) -638*a(n-15) -7762*a(n-16) +9656*a(n-17) +4185*a(n-18) -17112*a(n-19) -4552*a(n-20) +15815*a(n-21) +33775*a(n-22) -23312*a(n-23) -26945*a(n-24) -64119*a(n-25) +139962*a(n-26) +58933*a(n-27) -103605*a(n-28) -338619*a(n-29) +334975*a(n-30) +220898*a(n-31) +159008*a(n-32) -688281*a(n-33) +28868*a(n-34) +145506*a(n-35) +745193*a(n-36) +136204*a(n-37) -163467*a(n-38) -392203*a(n-39) -786507*a(n-40) -198043*a(n-41) +71402*a(n-42) +522504*a(n-43) -893490*a(n-44) -181709*a(n-45) -34798*a(n-46) +1298101*a(n-47) -389417*a(n-48) +272289*a(n-49) -131420*a(n-50) +429738*a(n-51) +86612*a(n-52) -28720*a(n-53) +228880*a(n-54) -528862*a(n-55) +88876*a(n-56) +140772*a(n-57) +250912*a(n-58) -221580*a(n-59) -172620*a(n-60) +248696*a(n-61) +38776*a(n-62) -21376*a(n-63) -9376*a(n-64) +32176*a(n-65) +6752*a(n-66) -42336*a(n-67) +30000*a(n-68) +2976*a(n-69) -12640*a(n-70) -1344*a(n-71) +2880*a(n-72) -768*a(n-73) -384*a(n-74).

A196135 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,3,4 for x=0,1,2,3,4.

Original entry on oeis.org

1, 14, 31, 165, 326, 1350, 3288, 12943, 33772, 113604, 328378, 1119797, 3245707, 10352649, 31244339, 100779085, 304866170, 952470015, 2927610616, 9231448285, 28362649959, 88098662332, 272473939620, 851211806848, 2631049299378
Offset: 1

Views

Author

R. H. Hardin Sep 28 2011

Keywords

Comments

Every 0 is next to 0 0's, every 1 is next to 1 2's, every 2 is next to 2 1's, every 3 is next to 3 3's, every 4 is next to 4 4's
Column 5 of A196138

Examples

			Some solutions for n=4
..0..1..2..0..1....1..0..2..1..1....2..1..0..2..1....2..1..1..2..1
..1..0..1..1..2....2..1..1..1..2....1..0..1..1..0....1..1..1..2..0
..2..1..1..1..0....2..1..1..1..2....1..1..2..0..1....1..2..0..1..1
..0..1..2..2..1....1..1..2..0..1....2..1..0..1..2....1..2..1..1..2
		

A196136 Number of nX6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,3,4 for x=0,1,2,3,4.

Original entry on oeis.org

1, 19, 70, 251, 1350, 3716, 20706, 63545, 255501, 992477, 3693353, 15143098, 54682695, 222402469, 838015799, 3238327921, 12552211666, 47967154876, 187109798637, 714494895572, 2773237529931, 10674786749417, 41144890359713
Offset: 1

Views

Author

R. H. Hardin Sep 28 2011

Keywords

Comments

Every 0 is next to 0 0's, every 1 is next to 1 2's, every 2 is next to 2 1's, every 3 is next to 3 3's, every 4 is next to 4 4's
Column 6 of A196138

Examples

			Some solutions for n=4
..0..1..2..0..2..1....2..1..0..1..2..0....1..1..2..2..1..0....1..1..0..2..1..1
..2..1..1..1..1..0....1..1..2..0..1..1....2..0..1..1..0..1....2..2..1..1..1..2
..1..1..0..2..1..1....0..1..1..1..0..2....1..1..0..1..2..2....1..0..1..1..1..2
..0..2..1..0..1..2....1..2..0..2..1..1....0..2..1..0..1..1....0..1..2..2..1..1
		

A196137 Number of nX7 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,2,1,3,4 for x=0,1,2,3,4.

Original entry on oeis.org

3, 46, 117, 931, 3288, 20706, 75720, 384083, 1662512, 8212668, 37172701, 176457313, 803299589, 3768617073, 17355787464, 81234030372, 376860933270, 1753580102111, 8135995110263, 37838340282830, 175764796211917, 817275191103917
Offset: 1

Views

Author

R. H. Hardin Sep 28 2011

Keywords

Comments

Every 0 is next to 0 0's, every 1 is next to 1 2's, every 2 is next to 2 1's, every 3 is next to 3 3's, every 4 is next to 4 4's
Column 7 of A196138

Examples

			Some solutions for n=4
..1..2..0..1..1..2..1....1..1..2..2..1..1..0....1..2..1..1..2..2..1
..0..1..1..2..0..2..1....2..0..1..1..0..2..1....1..2..1..0..1..1..1
..2..1..1..2..1..1..1....1..1..1..1..2..2..1....1..2..0..1..1..1..2
..1..0..1..2..1..1..2....1..2..2..1..1..1..0....0..1..1..2..2..1..0
		

A196131 Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 0,2,1,3,4 for x=0,1,2,3,4.

Original entry on oeis.org

1, 4, 4, 31, 326, 3716, 75720, 2040678, 86632050, 5257705657
Offset: 1

Views

Author

R. H. Hardin Sep 28 2011

Keywords

Comments

Every 0 is next to 0 0's, every 1 is next to 1 2's, every 2 is next to 2 1's, every 3 is next to 3 3's, every 4 is next to 4 4's
Diagonal of A196138

Examples

			Some solutions for n=4
..0..2..1..0....1..0..1..2....0..1..2..0....0..2..1..0....1..1..2..0
..1..1..1..2....2..1..0..1....2..1..1..1....1..1..1..2....2..0..1..1
..2..1..0..1....2..1..1..0....1..1..0..2....2..1..1..1....1..1..1..2
..0..1..2..1....1..0..2..1....0..2..1..1....0..1..2..0....0..2..1..0
		
Showing 1-7 of 7 results.