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

%I A283033 #24 Sep 08 2022 08:46:18
%S A283033 0,1,4211744,105918450471,140738033618944,37252918396015625,
%T A283033 3553786240466361696,167633579843887699759,4722366500530551259136,
%U A283033 89737248564744874067889,1250000000501250002500000,13543382431328404683826391,119245270812803151147085824
%N A283033 Number of inequivalent 5 X 5 matrices with entries in {1,2,3,...,n} up to rotations and reflections.
%C A283033 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.
%H A283033 G. C. Greubel, <a href="/A283033/b283033.txt">Table of n, a(n) for n = 0..1000</a>
%F A283033 a(n) = n^7*(n^18 + 4*n^8 + n^6 + 2)/8.
%F A283033 From _Chai Wah Wu_, Dec 07 2018: (Start)
%F A283033 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.
%F A283033 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)
%e A283033 For n=2 we get a(2)=4211744 inequivalent 5 X 5 binary matrices up to rotations and reflections.
%p A283033 [n^7*(n^18+4*n^8+n^6+2)/8$n=0..16]; # _Muniru A Asiru_, Dec 07 2018
%t A283033 Table[n^7 (n^18 + 4 n^8 + n^6 + 2)/8, {n, 0, 16}]
%o A283033 (PARI) a(n) = n^7*(n^18 + 4*n^8 + n^6 + 2)/8; \\ _Indranil Ghosh_, Feb 27 2017
%o A283033 (Python) def A283033(n): return n**7*(n**18 + 4*n**8 + n**6 + 2)/8 # _Indranil Ghosh_, Feb 27 2017
%o A283033 (Magma) [n^7*(n^18+4*n^8+n^6+2)/8: n in [0..20]]; // _G. C. Greubel_, Dec 07 2018
%o A283033 (Sage) [n^7*(n^18+4*n^8+n^6+2)/8 for n in range(20)] # _G. C. Greubel_, Dec 07 2018
%o A283033 (GAP) List([0..20], n -> n^7*(n^18+4*n^8+n^6+2)/8); # _G. C. Greubel_, Dec 07 2018
%Y A283033 Row n=5 of A343097.
%Y A283033 Cf. A282612, A282613, A282614, A283026, A283027, A283028, A283029, A283030, A283031, A283032.
%Y A283033 Cf. A217338 (4 X 4 version), A217331 (3 X 3 version), A002817 (2 X 2 version).
%K A283033 nonn
%O A283033 0,3
%A A283033 _David Nacin_, Feb 27 2017