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.

A204706 Number of (n+1)X(n+1) 0..1 arrays with the permanents of all 2X2 subblocks equal and nonzero.

Original entry on oeis.org

7, 33, 257, 3473, 73345, 2542369, 140090241, 12503757969, 1787244586881, 411927241028353, 152442345546739969, 90819596095626887105, 86960426240537811217921, 133963874202574308172821153
Offset: 1

Views

Author

R. H. Hardin Jan 18 2012

Keywords

Comments

Diagonal of A204713

Examples

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

Links

A204707 Number of (n+1) X 3 0..1 arrays with the permanents of all 2 X 2 subblocks equal and nonzero.

Original entry on oeis.org

13, 33, 81, 209, 529, 1361, 3473, 8913, 22801, 58449, 149649, 383441, 982033, 2515793, 6443921, 16507089, 42282769, 108311121, 277442193, 710686673, 1820455441, 4663202129, 11945023889, 30597832401, 78377927953, 200769257553
Offset: 1

Views

Author

R. H. Hardin, Jan 18 2012

Keywords

Comments

Column 2 of A204713.

Examples

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

Links

Crossrefs

Cf. A204713.

Formula

Empirical: a(n) = 2*a(n-1) +3*a(n-2) -4*a(n-3).
Conjectures from Colin Barker, Jun 09 2018: (Start)
G.f.: x*(13 + 7*x - 24*x^2) / ((1 - x)*(1 - x - 4*x^2)).
a(n) = 1 + (2^(-1-n)*((1-sqrt(17))^n*(-19+5*sqrt(17)) + (1+sqrt(17))^n*(19+5*sqrt(17)))) / sqrt(17).
(End)

A204708 Number of (n+1) X 4 0..1 arrays with the permanents of all 2 X 2 subblocks equal and nonzero.

Original entry on oeis.org

25, 81, 257, 833, 2689, 8705, 28161, 91137, 294913, 954369, 3088385, 9994241, 32342017, 104660993, 338690049, 1096024065, 3546808321, 11477712897, 37142659073, 120196169729, 388962975745, 1258710630401, 4073273163777
Offset: 1

Views

Author

R. H. Hardin, Jan 18 2012

Keywords

Comments

Column 3 of A204713.

Examples

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

Links

Crossrefs

Cf. A204713.

Formula

Empirical: a(n) = 3*a(n-1) +2*a(n-2) -4*a(n-3).
Conjectures from Colin Barker, Jun 09 2018: (Start)
G.f.: x*(25 + 6*x - 36*x^2) / ((1 - x)*(1 - 2*x - 4*x^2)).
a(n) = (5 + (20-8*sqrt(5))*(1-sqrt(5))^n + 4*(1+sqrt(5))^n*(5+2*sqrt(5))) / 5.
(End)

A204709 Number of (n+1) X 5 0..1 arrays with the permanents of all 2 X 2 subblocks equal and nonzero.

Original entry on oeis.org

49, 209, 833, 3473, 14145, 58449, 239425, 986129, 4047681, 16650449, 68397889, 281218705, 1155579713, 4750209361, 19522035521, 80241997073, 329789811521, 1355498530257, 5571139502913, 22898117877649, 94112790021953
Offset: 1

Views

Author

R. H. Hardin, Jan 18 2012

Keywords

Comments

Column 4 of A204713.

Examples

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

Links

Crossrefs

Cf. A204713.

Formula

Empirical: a(n) = a(n-1) +13*a(n-2) +3*a(n-3) -16*a(n-4).
Empirical g.f.: x*(49 + 160*x - 13*x^2 - 224*x^3) / ((1 - x)*(1 - 13*x^2 - 16*x^3)). - Colin Barker, Jun 09 2018

A204710 Number of (n+1) X 6 0..1 arrays with the permanents of all 2 X 2 subblocks equal and nonzero.

Original entry on oeis.org

97, 529, 2689, 14145, 73345, 382849, 1992321, 10382977, 54072961, 281700993, 1467309697, 7643513473, 39814841985, 207399103105, 1080347897473, 5627597738625, 29314404685441, 152700279978625, 795423120883329
Offset: 1

Views

Author

R. H. Hardin, Jan 18 2012

Keywords

Comments

Column 5 of A204713.

Examples

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

Links

Crossrefs

Cf. A204713.

Formula

Empirical: a(n) = 4*a(n-1) +15*a(n-2) -38*a(n-3) -52*a(n-4) +72*a(n-5).
Empirical g.f.: x*(97 + 141*x - 882*x^2 - 860*x^3 + 1576*x^4) / ((1 - x)*(1 + 2*x)*(1 - 5*x - 8*x^2 + 36*x^3)). - Colin Barker, Jun 09 2018

A204711 Number of (n+1)X7 0..1 arrays with the permanents of all 2X2 subblocks equal and nonzero.

Original entry on oeis.org

193, 1361, 8705, 58449, 382849, 2542369, 16748161, 110871041, 731709057, 4838473473, 31954317953, 211206670209, 1395251843713, 9220409667201, 60918293373569, 402541765541505, 2659689937121921, 17574356285235841
Offset: 1

Views

Author

R. H. Hardin, Jan 18 2012

Keywords

Comments

Column 6 of A204713

Examples

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

Links

Programs

  • Maple
    Configs:=  [seq(convert(2^7+i,base,2)[1..7],i=0..2^7-1)]:
Compatible:= proc(i,j)
if andmap(k -> Configs[i][k]*Configs[j][k+1]+Configs[i][k+1]*Configs[j][k] = 1, [$1..6]) then 1 else 0 fi
end proc:
T:= Matrix(128,128,Compatible):
u:= Vector[row](128, 1):
v:= Vector(128, 1):
TV[0]:= v:
for n from 1 to 40 do TV[n]:= T . TV[n-1] od:
seq(1+u . TV[n],n=1..40); # Robert Israel, Jun 11 2018

Formula

Empirical: a(n) = 4*a(n-1) +45*a(n-2) -126*a(n-3) -642*a(n-4) +1332*a(n-5) +3620*a(n-6) -5624*a(n-7) -6800*a(n-8) +8192*a(n-9).
Empirical formula confirmed by Robert Israel, Jun 11 2018: see link.

A204712 Number of (n+1) X 8 0..1 arrays with the permanents of all 2 X 2 subblocks equal and nonzero.

Original entry on oeis.org

385, 3473, 28161, 239425, 1992321, 16748161, 140090241, 1174759297, 9838208513, 82449830017, 690711971457, 5787565930753, 48489078457729, 406275347589249, 3403932556101121, 28520064001053825, 238954333647573121
Offset: 1

Views

Author

R. H. Hardin, Jan 18 2012

Keywords

Comments

Column 7 of A204713.

Examples

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

Links

Crossrefs

Cf. A204713.

Programs

  • Maple
    Configs:=  [seq(convert(2^8+i,base,2)[1..8],i=0..2^8-1)]:
Compatible:= proc(i,j)
if andmap(k -> Configs[i][k]*Configs[j][k+1]+Configs[i][k+1]*Configs[j][k] = 1, [$1..7]) then 1 else 0 fi
end proc:
T:= Matrix(256,256,Compatible):
u:= Vector[row](256, 1):
v:= Vector(256, 1):
TV[0]:= v:
for n from 1 to 30 do TV[n]:= T . TV[n-1] od:
seq(1+ u . TV[n],n=1..30); # Robert Israel, Jun 19 2018

Formula

Empirical: a(n) = 8*a(n-1) +50*a(n-2) -389*a(n-3) -790*a(n-4) +6534*a(n-5) +3836*a(n-6) -45232*a(n-7) +9360*a(n-8) +108928*a(n-9) -82304*a(n-10).
Empirical formula confirmed by Robert Israel, Jun 19 2018: see link.
Showing 1-7 of 7 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.