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 1-4 of 4 results.

A233505 Number of tilings of a 2 X 2 X n box using bricks of shape 3 X 1 X 1 and 2 X 1 X 1.

Original entry on oeis.org

1, 2, 9, 45, 201, 1062, 5564, 28859, 152012, 799387, 4202165, 22117465, 116385352, 612443308, 3223118545, 16961953022, 89264218645, 469766599585, 2472212575433, 13010374123502, 68468999197712, 360328057238019, 1896278913278432, 9979444454056631
Offset: 0

Views

Author

Alois P. Heinz, Dec 11 2013

Keywords

Links

Crossrefs

Cf. A000931, A129682, A219866, A219867, A233313, A233506, A233507, A233509.

Programs

  • Maple
    a:= n-> coeff(series((x^17 +3*x^16 -x^15 -5*x^14 +8*x^13 -8*x^12 -22*x^10 -20*x^9 -62*x^8 -20*x^7 -42*x^6 +18*x^5 +19*x^3 +x^2 +3*x -1)/(-x^20 -2*x^19 +2*x^18 +9*x^17 -12*x^16 +27*x^15 +41*x^14 +66*x^13 +62*x^12 +184*x^11 +76*x^10 +156*x^9 -92*x^8 +20*x^7 -141*x^6 +28*x^5 -62*x^4 +19*x^3 +5*x -1), x, n+1), x, n):
seq(a(n), n=0..40);

Formula

G.f.: (x^17 +3*x^16 -x^15 -5*x^14 +8*x^13 -8*x^12 -22*x^10 -20*x^9 -62*x^8 -20*x^7 -42*x^6 +18*x^5 +19*x^3 +x^2 +3*x -1) / (-x^20 -2*x^19 +2*x^18 +9*x^17 -12*x^16 +27*x^15 +41*x^14 +66*x^13 +62*x^12 +184*x^11 +76*x^10 +156*x^9 -92*x^8 +20*x^7 -141*x^6 +28*x^5 -62*x^4 +19*x^3 +5*x -1).

A233506 Number of tilings of a 3 X 3 X n box using bricks of shape 3 X 1 X 1 and 2 X 1 X 1.

Original entry on oeis.org

1, 14, 717, 62253, 4732061, 382882762, 31449389548, 2571574546111, 210607584419520, 17254476918858789, 1413637025226131703, 115812392270890399373, 9488271882367228634756, 777357166136453697810804, 63686950935296529029018801, 5217741644362129948411085318
Offset: 0

Views

Author

Alois P. Heinz, Dec 11 2013

Keywords

Links

Crossrefs

Cf. A000931, A129682, A219866, A219867, A233313, A233505, A233507, A233509.

Programs

  • Maple
    b:= proc(n, l) option remember; local k, t; t:= min(l[]);
      if n=0 then 1 elif t>0 then b(n-t, map(h->h-t, l))
    else for k while l[k]>0 do od;
         add(`if`(n>=j, b(n, s(k=j, l)), 0), j=2..3)+
         `if`(k<=6 and l[k+3]=0, b(n, s(k=1, k+3=1, l)), 0)+
         `if`(k<=3 and l[k+3]=0 and l[k+6]=0,
            b(n, s(k=1, k+3=1, k+6=1, l)), 0)+
         `if`(irem(k, 3)>0 and l[k+1]=0,
            b(n, s(k=1, k+1=1, l)), 0)+
         `if`(irem(k, 3)=1 and l[k+1]=0 and l[k+2]=0,
            b(n, subsop(k=1, k+1=1, k+2=1, l)), 0)
      fi
    end:
a:=n-> b(n, [0$9]): s:=subsop:
seq(a(n), n=0..10);
  • Mathematica
    b[n_, l_] := b[n, l] = Module[{k, t}, t := Min[l]; If [n == 0, 1, If[t > 0, b[n-t, l-t], k = 1; While[l[[k]] > 0, k++ ]; Sum[If[n >= j, b[n, ReplacePart[l, k -> j]], 0], {j, 2, 3}] + If[k <= 6 && l[[k+3]] == 0, b[n, ReplacePart[l, {k -> 1, k+3 -> 1}]], 0] + If[k <= 3 && l[[k+3]] == 0 && l[[k+6]] == 0, b[n, ReplacePart[l, {k -> 1, k+3 -> 1, k+6 -> 1}]], 0] + If[Mod[k, 3] > 0 && l[[k+1]] == 0, b[n, ReplacePart[l, {k -> 1, k+1 -> 1}]], 0] + If[Mod[k, 3] == 1 && l[[k+1]] == 0 && l[[k+2]] == 0, b[n, ReplacePart[l, {k -> 1, k+1 -> 1, k+2 -> 1}]], 0] ]] ]; a[n_] := b[n, Array[0&, 9]]; Table[a[n], {n, 0, 10}] // Flatten (* Jean-François Alcover, Dec 16 2013, translated from Maple *)

A233507 Number of tilings of a 2 X 4 X n box using bricks of shape 3 X 1 X 1 and 2 X 1 X 1.

Original entry on oeis.org

1, 7, 201, 9787, 379688, 16512483, 726964790, 31549810845, 1378740599284, 60239603421159, 2630166605483293, 114886450998314920, 5017916294582867990, 219163121582772423673, 9572435654283943792842, 418094220600909382190818, 18261053013117932038592765
Offset: 0

Views

Author

Alois P. Heinz, Dec 11 2013

Keywords

Examples

			a(1) = A219866(4,2) = A129682(4) = A219866(2,4) = A219862(2) = 7:
._______. ._______. ._______. ._______.
|_____| | | |_____| | | | | | |___| | |
|_____|_| |_|_____| |_|_|_|_| |___|_|_|
._______. ._______. ._______.
| |___| | | | |___| |___|___|
|_|___|_| |_|_|___| |___|___|.

Links

Crossrefs

Cf. A000931, A129682, A219866, A219867, A233313, A233505, A233506, A233509.

Programs

  • Maple
    b:= proc(n, l) option remember; local k, t; t:= min(l[]);
      if n=0 then 1
    elif t>0 then b(n-t, map(h->h-t, l))
    else for k while l[k]>0 do od;
         add(`if`(n>=j, b(n, s(k=j, l)), 0), j=2..3)+
         `if`(k<=6 and l[k+2]=0, b(n, s(k=1, k+2=1, l)), 0)+
         `if`(k<=4 and l[k+2]=0 and l[k+2*2]=0, b(n, s(k=1,
         k+2=1, k+2*2=1, l)), 0)+ `if`(irem(k, 2)>0 and
         l[k+1]=0, b(n, s(k=1, k+1=1, l)), 0)
      fi
    end:
a:=n-> b(n, [0$8]): s:= subsop:
seq(a(n), n=0..10);
  • Mathematica
    b[n_, l_] := b[n, l] = Module[{k, t}, t = Min[l]; Which[n == 0, 1, t > 0, b[n-t, l-t], True, For[k = 1, l[[k]] > 0, k++]; Sum[If[n >= j, b[n, ReplacePart[l, k -> j]], 0], {j, 2, 3}] + If[k <= 6 && l[[k + 2]] == 0, b[n, ReplacePart[l, {k -> 1, k+2 -> 1}]], 0] + If[k <= 4 && l[[k+2]] == 0 && l[[k+2*2]] == 0, b[n, ReplacePart[l, {k -> 1, k+2 -> 1, k+2*2 -> 1}]], 0] + If[Mod[k, 2] > 0 && l[[k+1]] == 0, b[n, ReplacePart[l, {k -> 1, k+1 -> 1}]], 0]]]; a[n_] := b[n, Array[0&, 8]]; Table[Print[an = a[n]]; an, {n, 0, 16}] (* Jean-François Alcover, Dec 30 2013, translated from Maple *)

A233509 Number of tilings of a 2 X 5 X n box using bricks of shape 3 X 1 X 1 and 2 X 1 X 1.

Original entry on oeis.org

1, 15, 1062, 148414, 16512483, 2043497465, 257251613508, 31941208907916, 3990164870713039, 498504394558488109, 62237975023439983192, 7773270324407375580946, 970802515607358269506951, 121240108673115249961266051, 15141593230837339625055971170
Offset: 0

Views

Author

Alois P. Heinz, Dec 11 2013

Keywords

Examples

			a(1) = A219866(5,2) = A129682(5) = A219866(2,5) = A219868(2) = 15:
.___.  .___.  .___.  .___.  .___.  .___.  .___.  .___.
| | |  |___|  | | |  |___|  | | |  |___|  | | |  |___|
| | |  |___|  |_|_|  | | |  | | |  |___|  |_|_|  | | |
|_|_|  |___|  |___|  |_|_|  |_|_|  |___|  |___|  |_|_|
| | |  | | |  | | |  | | |  |___|  |___|  |___|  |___|
|_|_|  |_|_|  |_|_|  |_|_|  |___|  |___|  |___|  |___|
.___.  .___.  .___.  .___.  .___.  .___.  .___.
| | |  | | |  |___|  |___|  | | |  | | |  |___|
|_|_|  |_|_|  |___|  |___|  |_| |  | |_|  | | |
| | |  | | |  | | |  | | |  | |_|  |_| |  | | |
| | |  |_|_|  | | |  |_|_|  | | |  | | |  |_|_|
|_|_|  |___|  |_|_|  |___|  |_|_|  |_|_|  |___|.

Links

Crossrefs

Cf. A000931, A129682, A219866, A219867, A233313, A233505, A233506, A233507.

Programs

  • Maple
    b:= proc(n, l) option remember; local k, t; t:= min(l[]);
      if n=0 then 1 elif t>0 then b(n-t, map(h->h-t, l))
    else for k while l[k]>0 do od;
         add(`if`(n>=j, b(n, s(k=j, l)), 0), j=2..3)+
         `if`(k<=5 and l[k+5]=0, b(n, s(k=1, k+5=1, l)), 0)+
         `if`(irem(k, 5)>0 and l[k+1]=0, b(n, s(k=1, k+1=1, l)), 0)+
         `if`(irem(k, 5) in [$1..3] and l[k+1]=0 and l[k+2]=0,
         b(n, s(k=1, k+1=1, k+2=1, l)), 0)
      fi
    end:
a:=n-> b(n, [0$10]): s:=subsop:
seq(a(n), n=0..4);
  • Mathematica
    b[n_, l_] := b[n, l] = Module[{k, t}, t = Min[l]; Which[n == 0, 1, t > 0, b[n-t, l-t], True, For[k = 1, l[[k]] > 0, k++]; Sum[If[n >= j, b[n, ReplacePart[l, k -> j]], 0], {j, 2, 3}] + If[k <= 5 && l[[k+5]] == 0, b[n, ReplacePart[l, {k -> 1, k+5 -> 1}]], 0] + If[Mod[k, 5] > 0 && l[[k+1]] == 0, b[n, ReplacePart[l, {k -> 1, k+1 -> 1}]], 0] + If[1 <= Mod[k, 5] <= 3 && l[[k+1]] == 0 && l[[k+2]] == 0, b[n, ReplacePart[l, {k -> 1, k+1 -> 1, k+2 -> 1}]], 0]]];a[n_] := b[n, Array[0&, 10]]; Table[Print[an = a[n]]; an, {n, 0, 14}] (* Jean-François Alcover, Dec 30 2013, translated from Maple *)
Showing 1-4 of 4 results.

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