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 1-3 of 3 results.

A204237 Symmetric matrix given by f(i,j)=max(3i-j,3j-i).

Original entry on oeis.org

2, 5, 5, 8, 4, 8, 11, 7, 7, 11, 14, 10, 6, 10, 14, 17, 13, 9, 9, 13, 17, 20, 16, 12, 8, 12, 16, 20, 23, 19, 15, 11, 11, 15, 19, 23, 26, 22, 18, 14, 10, 14, 18, 22, 26, 29, 25, 21, 17, 13, 13, 17, 21, 25, 29, 32, 28, 24, 20, 16, 12, 16, 20, 24, 28, 32, 35, 31, 27, 23
Offset: 1

Views

Author

Clark Kimberling, Jan 13 2012

Keywords

Examples

			Northwest corner:
2....5....8....11...14...17
5....4....7....10...13...16
8....7....6....9....12...15
11...10...9....8....11...14
14...13...12...11...10...13

Crossrefs

Cf. A204238, A204239.

Programs

  • Mathematica
    f[i_, j_] := Max[3 i - j, 3 j - i];
m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
TableForm[m[8]] (* 8x8 principal submatrix *)
Flatten[Table[f[i, n + 1 - i],
  {n, 1, 12}, {i, 1, n}]]  (* A204237 *)
Table[Det[m[n]], {n, 1, 22}]  (* A204238 *)
Permanent[m_] :=
  With[{a = Array[x, Length[m]]},
   Coefficient[Times @@ (m.a), Times @@ a]];
Table[Permanent[m[n]], {n, 1, 14}] (* A204239 *)

A204238 Determinant of the n-th principal submatrix of A204237.

Original entry on oeis.org

2, -17, 104, -560, 2816, -13568, 63488, -290816, 1310720, -5832704, 25690112, -112197632, 486539264, -2097152000, 8992587776, -38386270208, 163208757248, -691489734656, 2920577761280, -12300786335744, 51677046505472, -216603790671872, 905997581287424
Offset: 1

Views

Author

Clark Kimberling, Jan 13 2012

Keywords

Links

Crossrefs

Cf. A204237, A204239.

Programs

  • Mathematica
    f[i_, j_] := Max[3 i - j, 3 j - i];
m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
TableForm[m[8]] (* 8x8 principal submatrix *)
Flatten[Table[f[i, n + 1 - i],
  {n, 1, 12}, {i, 1, n}]]     (* A204237 *)
Table[Det[m[n]], {n, 1, 22}]  (* A204238 *)
Permanent[m_] :=
  With[{a = Array[x, Length[m]]},
   Coefficient[Times @@ (m.a), Times @@ a]];
Table[Permanent[m[n]], {n, 1, 14}] (* A204239 *)
  • PARI
    vector(20, n, matdet(matrix(n, n, i, j, max(3*i-j, 3*j-i)))) \\ Colin Barker, Feb 21 2015

Formula

Conjectures from Colin Barker, Feb 21 2015: (Start)
a(n) = -8*a(n-1)-16*a(n-2).
G.f. -x*(x-2) / (4*x+1)^2.
(End)

A204440 Permanent of the n-th principal submatrix of A204439.

Original entry on oeis.org

1, 1, 1, 2, 6, 20, 80, 384, 2016, 12096, 82080, 597888, 4783104, 41886720, 389145600, 3891456000, 41803776000, 472283136000, 5667397632000, 72153317376000, 959814696960000, 13437405757440000, 197840194965504000, 3028176742219776000, 48450827875516416000
Offset: 0

Views

Author

Clark Kimberling, Jan 15 2012

Keywords

Comments

Also the number of permutations pi in S_n such that pi(i) + i != 1 (mod 3) for all i. - Peter Kagey, Jan 25 2021

Crossrefs

Cf. A204239, A204435.

Programs

  • Mathematica
    f[i_, j_] := Mod[(2 + i + j)^2, 3];
m[n_] := Table[f[i, j], {i, 1, n}, {j, 1, n}]
TableForm[m[8]] (* 8x8 principal submatrix *)
Flatten[Table[f[i, n + 1 - i],
  {n, 1, 14}, {i, 1, n}]]           (* A204439 *)
Join[{1},Table[Permanent[m[n]], {n, 1, 22}]]  (* A204440 *)

Extensions

Typo in name corrected by Michel Marcus, Nov 11 2016
a(0) and a(23)-a(24) from Pontus von Brömssen, Jan 29 2021
Showing 1-3 of 3 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.