A283030 Number of inequivalent 5 X 5 matrices with entries in {1,2,3,...,n} up to row permutations.

0, 1, 376992, 7355513529, 9474438804480, 2491483056641250, 237223883948569056, 11182222570880983622, 314920519245916176384, 5983496429606726016735, 83341666958337500020000, 902948225666983587054711, 7950004204832195461143552, 58805000552467321853765064

Offset

0,3

Comments

Cycle index of symmetric group S4 on the set of 25 entries is (10*s(2)^5*s(1)^15 + 20*s(3)^5*s(1)^10 + 15*s(2)^10*s(1)^5 + 30*s(4)^5*s(1)^5 + 20*s(2)^5*s(3)^5 + 24*s(5)^5+s(1)^25)/120.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

a(n) = (n^25 + 10*n^20 + 35*n^15 + 50*n^10 + 24*n^5)/120.

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

a(n) = 26*a(n-1) - 325*a(n-2) + 2600*a(n-3) - 14950*a(n-4) + 65780*a(n-5) - 230230*a(n-6) + 657800*a(n-7) - 1562275*a(n-8) + 3124550*a(n-9) - 5311735*a(n-10) + 7726160*a(n-11) - 9657700*a(n-12) + 10400600*a(n-13) - 9657700*a(n-14) + 7726160*a(n-15) - 5311735*a(n-16) + 3124550*a(n-17) - 1562275*a(n-18) + 657800*a(n-19) - 230230*a(n-20) + 65780*a(n-21) - 14950*a(n-22) + 2600*a(n-23) - 325*a(n-24) + 26*a(n-25) - a(n-26) for n > 25.

G.f.: x*(201376*x^23 + 6769097812*x^22 + 9115118766616*x^21 + 2236218775591321*x^20 + 175251248958400030*x^19 + 5797456665826176046*x^18 + 94937993285056078902*x^17 + 849635569433212953261*x^16 + 4430970723887327210136*x^15 + 14044903652456409705760*x^14 + 27788396155245137222056*x^13 + 34830392581327241688322*x^12 + 27788479931754180338596*x^11 + 14044908029988217540516*x^10 + 4430933630938187561140*x^9 + 849629302807069561746*x^8 + 94943797840269544152*x^7 + 5799609980863901436*x^6 + 175505398388141776*x^5 + 2247537209457445*x^4 + 9283317972526*x^3 + 7345712062*x^2 + 376966*x + 1)/(x - 1)^26. (End)

Example

For n=2 we get a(2)=376992 inequivalent 5 X 5 binary matrices up to row permutations.

Maple

[(10*n^20+35*n^15+50*n^10+24*n^5+n^25)/120$n=0..16]; # Muniru A Asiru, Dec 07 2018

Mathematica

Table[(10n^20+ 35n^15 + 50n^10 + 24n^5 + n^25)/120, {n, 0, 16}]

Prog

(PARI) a(n) = (10*n^20 + 35*n^15 + 50*n^10 + 24*n^5 + n^25)/120; \\ Indranil Ghosh, Feb 27 2017
(Python) def A283030(n): return (10*n**20 + 35*n**15 + 50*n**10 + 24*n**5 + n**25)/120 # Indranil Ghosh, Feb 27 2017
(Magma) [n^5*(n^20 +10*n^15 +35*n^10 +50*n^5 +24)/120: n in [0..20]]; // G. C. Greubel, Dec 07 2018
(Sage) [n^5*(n^20 +10*n^15 +35*n^10 +50*n^5 +24)/120 for n in range(20)] # G. C. Greubel, Dec 07 2018
(GAP) List([0..20], n -> n^5*(n^20 +10*n^15 +35*n^10 +50*n^5 +24)/120); # G. C. Greubel, Dec 07 2018

Crossrefs

Cf. A282613, A282614, A283027, A283028, A283029, A283031, A283032, A283033.

Cf. A283026 (4 X 4 version), A282612 (3 X 3 version), A037270 (2 X 2 version).

Sequence in context: A218398 A089444 A203740 * A318964 A226361 A238078

Adjacent sequences: A283027 A283028 A283029 * A283031 A283032 A283033

Keyword

nonn,easy

Author

David Nacin, Feb 27 2017

Status

approved