A283026 Number of inequivalent 4 X 4 matrices with entries in {1,2,3,..,n} up to row permutations.

0, 1, 3876, 1929501, 183181376, 6419043125, 118091211876, 1388168405001, 11745311589376, 77279801651001, 416916712502500, 1915356782994501, 7705740009485376, 27731516944463501, 90762229896563876, 273716119247180625, 768684707117285376, 2027695320242670001

Offset

0,3

Comments

Cycle index of symmetry group S4 acting on the 16 entries is (6*s(2)^4s(1)^8 + 8*s(3)^4s(1)^4 + 3*s(2)^8 + 6*s(4)^4 + s(1)^{16})/24.

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = n^4*(n^4 + 1)*(n^4 + 2)*(n^4 + 3)/24.

From Chai Wah Wu, Dec 07 2018: (Start)

a(n) = 17*a(n-1) - 136*a(n-2) + 680*a(n-3) - 2380*a(n-4) + 6188*a(n-5) - 12376*a(n-6) + 19448*a(n-7) - 24310*a(n-8) + 24310*a(n-9) - 19448*a(n-10) + 12376*a(n-11) - 6188*a(n-12) + 2380*a(n-13) - 680*a(n-14) + 136*a(n-15) - 17*a(n-16) + a(n-17) for n > 16.

G.f.: -x*(x + 1)*(x^14 + 3858*x^13 + 1859887*x^12 + 149046428*x^11 + 3415692141*x^10 + 29161611758*x^9 + 104450960739*x^8 + 161533106376*x^7 + 104450960739*x^6 + 29161611758*x^5 + 3415692141*x^4 + 149046428*x^3 + 1859887*x^2 + 3858*x + 1)/(x - 1)^17. (End)

Example

For n=2 we get a(2)=3876 inequivalent 4x4 binary matrices up to row permutations.

Mathematica

Table[n^4*(n^4 + 1)*(n^4 + 2)*(n^4 + 3)/24, {n, 0, 30}]

Prog

(PARI) a(n) = n^4*(n^4 + 1)*(n^4 + 2)*(n^4 + 3)/24; \\ Indranil Ghosh, Feb 27 2017
(Python) def A283026(n) : return n**4*(n**4 + 1)*(n**4 + 2)*(n**4 + 3)/24 # Indranil Ghosh, Feb 27 2017

Crossrefs

Cf. A282613, A282614, A283027, A283028, A283029, A283031, A283032, A283033. A283030 (5x5 version). A282612 (3x3 version). A037270 (2x2 version).

Sequence in context: A108005 A065696 A246735 * A014891 A253484 A253479

Adjacent sequences: A283023 A283024 A283025 * A283027 A283028 A283029

Keyword

easy,nonn

Author

David Nacin, Feb 27 2017

Status

approved