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.

A206465 Number of (n+1)X(n+1) 0..2 arrays with every 2X2 subblock having zero permanent.

Original entry on oeis.org

25, 1411, 110889, 68352739, 61244865529, 377599682448675, 3848918441303655721, 232902549300945882026755, 26631802795003317433250214201, 15822211869785299795988010016362883
Offset: 1

Views

Author

R. H. Hardin Feb 08 2012

Keywords

Comments

Diagonal of A206472

Examples

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

A206466 Number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock having zero permanent.

Original entry on oeis.org

121, 1411, 11025, 106891, 958441, 8963667, 82609921, 767387611, 7109019225, 65954564131, 611588125681, 5672733227307, 52611971134921, 487976540781811, 4525907460768225, 41977494854894971, 389337236836785721
Offset: 1

Views

Author

R. H. Hardin, Feb 08 2012

Keywords

Comments

Column 2 of A206472.

Examples

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

Crossrefs

Cf. A206472.

Formula

Empirical: a(n) = 11*a(n-1) - 176*a(n-3) + 256*a(n-4).
Empirical g.f.: x*(121 + 80*x - 4496*x^2 + 6912*x^3) / ((1 - 4*x)*(1 + 4*x)*(1 - 11*x + 16*x^2)). - Colin Barker, Jun 16 2018

A206467 Number of (n+1) X 4 0..2 arrays with every 2 X 2 subblock having zero permanent.

Original entry on oeis.org

441, 11025, 110889, 1896129, 23707161, 356190129, 4803737481, 69030731169, 955680252921, 13523866505361, 188928681187689, 2659384141993089, 37267791691450329, 523625523775949169, 7345838128808607561
Offset: 1

Views

Author

R. H. Hardin, Feb 08 2012

Keywords

Comments

Column 3 of A206472.

Examples

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

Crossrefs

Cf. A206472.

Formula

Empirical: a(n) = 15*a(n-1) + 54*a(n-2) - 1116*a(n-3) + 1728*a(n-4) + 10368*a(n-5) - 20736*a(n-6).
Empirical g.f.: 9*x*(49 + 490*x - 8700*x^2 + 14400*x^3 + 91008*x^4 - 186624*x^5) / ((1 - 21*x + 108*x^2 - 144*x^3)*(1 + 6*x - 36*x^2 - 144*x^3)). - Colin Barker, Jun 16 2018

A206468 Number of (n+1)X5 0..2 arrays with every 2X2 subblock having zero permanent.

Original entry on oeis.org

1849, 106891, 1896129, 68352739, 1693734025, 52552339515, 1457044540561, 43214597865811, 1240051361495769, 36294544907153707, 1052106476736321889, 30674877583244503491, 891844034416624515625, 25973093752500918767899
Offset: 1

Views

Author

R. H. Hardin Feb 08 2012

Keywords

Comments

Column 4 of A206472

Examples

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

Formula

Empirical: a(n) = 39*a(n-1) -11348*a(n-3) +76272*a(n-4) +429792*a(n-5) -3994496*a(n-6) +37171200*a(n-8) -43614208*a(n-9)

A206469 Number of (n+1)X6 0..2 arrays with every 2X2 subblock having zero permanent.

Original entry on oeis.org

7225, 958441, 23707161, 1693734025, 61244865529, 3420616959081, 144660587865049, 7310031634630729, 329657818912939449, 15990423345433902121, 740325481079134598041, 35313542504161253544969
Offset: 1

Views

Author

R. H. Hardin Feb 08 2012

Keywords

Comments

Column 5 of A206472

Examples

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

Formula

Empirical: a(n) = 55*a(n-1) +978*a(n-2) -78848*a(n-3) +185192*a(n-4) +32350560*a(n-5) -254580608*a(n-6) -5080783360*a(n-7) +56605956096*a(n-8) +280495972352*a(n-9) -4555145707520*a(n-10) -1650631114752*a(n-11) +144197302616064*a(n-12) -230333727375360*a(n-13) -1370695862845440*a(n-14) +3206175906594816*a(n-15)

A206470 Number of (n+1)X7 0..2 arrays with every 2X2 subblock having zero permanent.

Original entry on oeis.org

29241, 8963667, 356190129, 52552339515, 3420616959081, 377599682448675, 30374762423377761, 2996776279527835851, 262356222717008105625, 24807486299199737090355, 2243325257562176033089041
Offset: 1

Views

Author

R. H. Hardin Feb 08 2012

Keywords

Comments

Column 6 of A206472

Examples

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

Formula

Empirical: a(n) = 147*a(n-1) -783720*a(n-3) +22720320*a(n-4) +1208991744*a(n-5) -54468142848*a(n-6) -614613775104*a(n-7) +51672615856128*a(n-8) -95234427260928*a(n-9) -23998259218120704*a(n-10) +201605913386680320*a(n-11) +5689361505992048640*a(n-12) -76294817096637874176*a(n-13) -628017046749267886080*a(n-14) +13195491648030973624320*a(n-15) +14645283042051703701504*a(n-16) -1131405415550428045639680*a(n-17) +2665553144520224318423040*a(n-18) +45873154851254425563955200*a(n-19) -208791793059186748686336000*a(n-20) -694038525930408939356160000*a(n-21) +5010428057070448693739520000*a(n-22) -38126822008840601972244480000*a(n-24) +51697385774699121318297600000*a(n-25)

A206471 Number of (n+1)X8 0..2 arrays with every 2X2 subblock having zero permanent.

Original entry on oeis.org

116281, 82609921, 4803737481, 1457044540561, 144660587865049, 30374762423377761, 3848918441303655721, 685519912635644947249, 97075380100800976220025, 16048326634124121062046721
Offset: 1

Views

Author

R. H. Hardin Feb 08 2012

Keywords

Comments

Column 7 of A206472

Examples

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

Formula

Empirical: a(n) = 187*a(n-1) +16890*a(n-2) -4251100*a(n-3) -40650128*a(n-4) +34942108176*a(n-5) -509473309952*a(n-6) -143301983645440*a(n-7) +3781912316451840*a(n-8) +331477180236791808*a(n-9) -11437248501456273408*a(n-10) -456953450334995742720*a(n-11) +19427954988478986715136*a(n-12) +378498296435438535049216*a(n-13) -20467094815444348981739520*a(n-14) -176626051842769499929444352*a(n-15) +13996085228807881237465137152*a(n-16) +30568383723039618710120693760*a(n-17) -6355164028117009141540627415040*a(n-18) +12457938945007485052056640684032*a(n-19) +1929828810876076957792938988929024*a(n-20) -9299483116586836848017963795611648*a(n-21) -389157136861521793604550385668718592*a(n-22) +2708325225472310296274920611243884544*a(n-23) +50924689860837777608863804409805537280*a(n-24) -447452547804564001571380763718647283712*a(n-25) -4125665523625190917601565450289790582784*a(n-26) +44428660564874781732775601609703285587968*a(n-27) +186837790537674954483787089018593126383616*a(n-28) -2618004719714992257591615094837678769700864*a(n-29) -3397132551485027226296690950170149841272832*a(n-30) +86176350300963117293366090863279754170073088*a(n-31) -38719009409154496417441531127358038313271296*a(n-32) -1390107790923631754160207042472622108971106304*a(n-33) +2057972867841973929472259334257306497261240320*a(n-34) +7785693287184378683612676651109988061281255424*a(n-35) -15061387791262419693934415229148488062591827968*a(n-36)
Showing 1-7 of 7 results.