A283029 Number of inequivalent 5 X 5 matrices with entries in {1,2,3,..,n} when a matrix and its transpose are considered equivalent.

0, 1, 16793600, 423651479175, 562950490292224, 149011627197265625, 14215144250057342976, 670534312205763205375, 18889465949070766899200, 358948993948871860432449, 5000000000500000000000000, 54173529719030485105622951, 476981083228048575587942400

Offset

0,3

Comments

Cycle index of symmetric group S2 acting on the set of 25 entries is (s(2)^10*s(1)^5 + s(1)^25)/2.

Links

Table of n, a(n) for n=0..12.

Formula

a(n) = n^15*(n^2+1)*(n^8-n^6+n^4-n^2+1)/2.

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*(x^24 + 16793574*x^23 + 423214845900*x^22 + 551941009751074*x^21 + 134512557517054626*x^20 + 10522699609491808746*x^19 + 347912001753554722204*x^18 + 5696453728178627889150*x^17 + 50977946159336791604079*x^16 + 265857130683340877431996*x^15 + 842694350441988138095256*x^14 + 1667306282568523129263444*x^13 + 2089823554970188253479900*x^12 + 1667306282568523129263444*x^11 + 842694350441988138095256*x^10 + 265857130683340877431996*x^9 + 50977946159336791604079*x^8 + 5696453728178627889150*x^7 + 347912001753554722204*x^6 + 10522699609491808746*x^5 + 134512557517054626*x^4 + 551941009751074*x^3 + 423214845900*x^2 + 16793574*x + 1)/(x - 1)^26. (End)

Example

For n=2 we get a(2)=16793600 inequivalent 5x5 binary matrices up to the action of transposition.

Mathematica

Table[n^15 (n^2 + 1) (n^8 - n^6 + n^4 - n^2 + 1)/2, {n, 0, 12}]

Prog

(PARI) a(n) = n^15*(n^2+1)*(n^8-n^6+n^4-n^2+1)/2; \\ Indranil Ghosh, Feb 27 2017
(Python) def A283029(n): return n**15*(n**2+1)*(n**8-n**6+n**4-n**2+1)/2 # Indranil Ghosh, Feb 27 2017

Crossrefs

Cf. A282612,A282613,A282614. A283026, A283027, A283028, A283030, A283031, A283032, A283033. A170798 (4x4 version). A168555 (3x3 version). A019582 (2x2 version)

Sequence in context: A013972 A036102 A230636 * A250933 A143510 A043680

Adjacent sequences: A283026 A283027 A283028 * A283030 A283031 A283032

Keyword

nonn,easy

Author

David Nacin, Feb 27 2017

Status

approved