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 1-6 of 6 results.

A230648 Number of nX4 0..2 white square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value 2-x(i,j).

Original entry on oeis.org

0, 9, 21, 123, 531, 2547, 11745, 54957, 255753, 1192623, 5557191, 25901847, 120714693, 562609041, 2622085629, 12220512675, 56954899323, 265444104699, 1237128910377, 5765764156725, 26871924749169, 125239314486231
Offset: 1

Views

Author

R. H. Hardin, Oct 27 2013

Keywords

Comments

Column 4 of A230652

Examples

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

Formula

Empirical: a(n) = 3*a(n-1) +8*a(n-2) -a(n-3) -a(n-4) for n>5.
Empirical: G.f. 3*x^2*(1+x)*(x^2-5*x+3) / ( 1-3*x-8*x^2+x^3+x^4 ). - R. J. Mathar, Oct 27 2013

A230650 Number of nX6 0..2 white square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value 2-x(i,j).

Original entry on oeis.org

0, 33, 177, 2547, 28161, 337977, 3951657, 46564959, 547445439, 6440488155, 75754392573, 891094042215, 10481688337035, 123293830743177, 1450276232412603, 17059265522993919, 200664184001736495
Offset: 1

Views

Author

R. H. Hardin, Oct 27 2013

Keywords

Comments

Column 6 of A230652

Examples

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

Formula

Empirical: a(n) = 8*a(n-1) +50*a(n-2) -22*a(n-3) -437*a(n-4) -1133*a(n-5) -548*a(n-6) +2623*a(n-7) +5757*a(n-8) +6227*a(n-9) -194*a(n-10) -2664*a(n-11) -3827*a(n-12) +2327*a(n-13) -5991*a(n-14) -4452*a(n-15) -3865*a(n-16) -6535*a(n-17) -536*a(n-18) -639*a(n-19) -373*a(n-20) -29*a(n-21) +76*a(n-22) -16*a(n-23) for n>24

A230647 Number of nX3 0..2 white square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value 2-x(i,j).

Original entry on oeis.org

0, 3, 3, 21, 27, 177, 231, 1509, 1971, 12873, 16815, 109821, 143451, 936897, 1223799, 7992789, 10440387, 68187513, 89068287, 581716461, 759853035, 4962698097, 6482404167, 42337417029, 55302225363, 361185960873, 471790411599
Offset: 1

Views

Author

R. H. Hardin, Oct 27 2013

Keywords

Comments

Column 3 of A230652

Examples

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

Formula

Empirical: a(n) = 9*a(n-2) -4*a(n-4).
Empirical: G.f. -3*x^2*(2*x+1)*(x-1) / ( 1-9*x^2+4*x^4 ). - R. J. Mathar, Oct 27 2013

A230649 Number of nX5 0..2 white square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value 2-x(i,j).

Original entry on oeis.org

0, 15, 27, 531, 1635, 28161, 90393, 1539207, 4956927, 84335553, 271665969, 4621740687, 14888070495, 253283346081, 815905965057, 13880597644287, 44713811014239, 760693546670625, 2450435395047009, 41688023124390687
Offset: 1

Views

Author

R. H. Hardin, Oct 27 2013

Keywords

Comments

Column 5 of A230652

Examples

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

Formula

Empirical: a(n) = 59*a(n-2) -230*a(n-4) -2*a(n-6) +32*a(n-8) for n>11

A230651 Number of nX7 0..2 white square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value 2-x(i,j).

Original entry on oeis.org

0, 63, 231, 11745, 90393, 3951657, 31908483, 1374288243, 11150938215, 479621050353, 3893231603781, 167435671598913, 1359174652590399, 58453268091967479, 474501281118252903, 20406595554618417837
Offset: 1

Views

Author

R. H. Hardin, Oct 27 2013

Keywords

Comments

Column 7 of A230652

Examples

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

Formula

Empirical: a(n) = 390*a(n-2) -14687*a(n-4) +146138*a(n-6) -823339*a(n-8) -2774563*a(n-10) +26807114*a(n-12) -60400888*a(n-14) +106367378*a(n-16) -35490451*a(n-18) -7548040169*a(n-20) +1542760687*a(n-22) +7961883650*a(n-24) +3473400076*a(n-26) +61902164677*a(n-28) +25546220017*a(n-30) +84369583536*a(n-32) +75320917456*a(n-34) +42723111397*a(n-36) -5387877662*a(n-38) +926204972*a(n-40) -121037200*a(n-42) +10124352*a(n-44) +414720*a(n-46) for n>47

A230646 Number of n X n 0..2 white square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value 2-x(i,j).

Original entry on oeis.org

0, 3, 3, 123, 1635, 337977, 31908483, 40860127671, 24818871787539, 201844710508818147, 781457119775191627041, 40464088148356899296269059, 997750456877626717987299707229
Offset: 1

Views

Author

R. H. Hardin, Oct 27 2013

Keywords

Comments

Diagonal of A230652

Examples

			Some solutions for n=5
..0..x..0..x..2....1..x..2..x..2....0..x..0..x..1....2..x..2..x..0
..x..2..x..0..x....x..1..x..0..x....x..2..x..1..x....x..0..x..2..x
..0..x..2..x..2....2..x..2..x..1....2..x..0..x..1....2..x..1..x..0
..x..1..x..2..x....x..0..x..1..x....x..0..x..1..x....x..1..x..0..x
..1..x..0..x..0....2..x..1..x..1....2..x..2..x..1....1..x..1..x..2
		
Showing 1-6 of 6 results.