A283033 Number of inequivalent 5 X 5 matrices with entries in {1,2,3,...,n} up to rotations and reflections.

0, 1, 4211744, 105918450471, 140738033618944, 37252918396015625, 3553786240466361696, 167633579843887699759, 4722366500530551259136, 89737248564744874067889, 1250000000501250002500000, 13543382431328404683826391, 119245270812803151147085824

Offset: 0

Author

David Nacin, Feb 27 2017

Keywords

• nonn

Comments

Cycle index of dihedral group D4 acting on the 25 entries is (2*s(4)^6*s(1) + s(2)^{12}*s(1) + 4*s(2)^10*s(1)^5 + s(1)^25)/8.

Examples

			For n=2 we get a(2)=4211744 inequivalent 5 X 5 binary matrices up to rotations and reflections.
		

Links

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

Crossrefs

Row n=5 of A343097.

Cf. A282612, A282613, A282614, A283026, A283027, A283028, A283029, A283030, A283031, A283032.

Cf. A217338 (4 X 4 version), A217331 (3 X 3 version), A002817 (2 X 2 version).

Programs

GAP

List([0..20], n -> n^7*(n^18+4*n^8+n^6+2)/8); # G. C. Greubel, Dec 07 2018

Magma

[n^7*(n^18+4*n^8+n^6+2)/8: n in [0..20]]; // G. C. Greubel, Dec 07 2018

Maple

[n^7*(n^18+4*n^8+n^6+2)/8$n=0..16]; # Muniru A Asiru, Dec 07 2018

Mathematica

Table[n^7 (n^18 + 4 n^8 + n^6 + 2)/8, {n, 0, 16}]

PARI

a(n) = n^7*(n^18 + 4*n^8 + n^6 + 2)/8; \\ Indranil Ghosh, Feb 27 2017

Python

def A283033(n): return n**7*(n**18 + 4*n**8 + n**6 + 2)/8 # Indranil Ghosh, Feb 27 2017

Sage

[n^7*(n^18+4*n^8+n^6+2)/8 for n in range(20)] # G. C. Greubel, Dec 07 2018

Formula

a(n) = n^7*(n^18 + 4*n^8 + n^6 + 2)/8.

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 + 4211718*x^23 + 105808945452*x^22 + 137985522720898*x^21 + 33628142067806706*x^20 + 2630674898090394666*x^19 + 86978000386844370748*x^18 + 1424113432167998385342*x^17 + 12744486540004851097263*x^16 + 66464282669989885009756*x^15 + 210673587611186802329496*x^14 + 416826570643036689533748*x^13 + 522455888740564118388412*x^12 + 416826570643036689533748*x^11 + 210673587611186802329496*x^10 + 66464282669989885009756*x^9 + 12744486540004851097263*x^8 + 1424113432167998385342*x^7 + 86978000386844370748*x^6 + 2630674898090394666*x^5 + 33628142067806706*x^4 + 137985522720898*x^3 + 105808945452*x^2 + 4211718*x + 1)/(x - 1)^26. (End)