The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A283028 Number of inequivalent 4 X 4 matrices with entries in {1,2,3,...,n} up to vertical and horizontal reflections. 8
 0, 1, 16576, 10766601, 1073790976, 38147265625, 705278736576, 8308236966001, 70368756760576, 463255079498001, 2500000075000000, 11487432626662201, 46221065046245376, 166354152907593001, 544488335559184576, 1642102090850390625, 4611686021648613376 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Cycle index of dihedral group D2 acting on the 16 entries is (3s(2)^8 + s(1)^16)/4. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (17, -136, 680, -2380, 6188, -12376, 19448, -24310, 24310, -19448, 12376, -6188, 2380, -680, 136, -17, 1). FORMULA a(n) = n^8 * (n^8 + 3)/4. 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 + 16558*x^13 + 10468387*x^12 + 882544028*x^11 + 20463263441*x^10 + 175065686258*x^9 + 626804969739*x^8 + 968894839176*x^7 + 626804969739*x^6 + 175065686258*x^5 + 20463263441*x^4 + 882544028*x^3 + 10468387*x^2 + 16558*x + 1)/(x - 1)^17. (End) E.g.f.: (1/4)*x*exp(x)*(x^15 + 120*x^14 + 6020*x^13 + 165620*x^12 + 2757118*x^11 + 28936908*x^10 + 193754990*x^9 + 820784250*x^8 + 2141764056*x^7 + 3281882688*x^6 + 2734927356*x^5 + 1096193700*x^4 + 171804004*x^3 + 7144584*x^2 + 33148*x + 4). - Stefano Spezia, Dec 07 2018 EXAMPLE For n=2 we get a(2)=16576 inequivalent 4 X 4 binary matrices up to vertical and horizontal reflections. MAPLE [n^8*(n^8+3)/4\$n=0..18]; # Muniru A Asiru, Dec 07 2018 MATHEMATICA Table[n^8(n^8 + 3)/4, {n, 0, 30}] PROG (PARI) a(n) = n^8 * (n^8 + 3)/4; \\ Altug Alkan, Feb 27 2017 (Python) def A283028(n): return n**8*(n**8 + 3)/4 # Indranil Ghosh, Feb 27 2017 (Magma) [n^8*(n^8+3)/4: n in [0..20]]; // G. C. Greubel, Dec 07 2018 (Sage) [n^8*(n^8+3)/4 for n in range(20)] # G. C. Greubel, Dec 07 2018 (GAP) List([0..20], n -> n^8*(n^8+3)/4); # G. C. Greubel, Dec 07 2018 CROSSREFS Cf. A282612, A282613, A283026, A283027, A283029, A283030, A283031, A283033. Cf. A283032 (5 X 5 version), A282614 (3 X 3 version), A039623 (2 X 2 version). Sequence in context: A193244 A240901 A234894 * A344241 A344242 A234374 Adjacent sequences: A283025 A283026 A283027 * A283029 A283030 A283031 KEYWORD nonn,easy AUTHOR David Nacin, Feb 27 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 8 17:58 EST 2023. Contains 367680 sequences. (Running on oeis4.)