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 A217574 (n^2)*(n^2-1)*(n^2-2)*(n^2-3). 1
 0, 0, 24, 3024, 43680, 303600, 1413720, 5085024, 15249024, 39929760, 94109400, 203889840, 412293024, 787083024, 1431033240, 2495102400, 4195023360, 6831849024, 10817040024, 16702719120, 25217757600, 37310399280, 54198168024, 77425845024, 108932342400 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Number of n X n matrices using all elements of {1,2,3,4} exactly once with other entries zero. [clarified by Debashish Sharma, Oct 13 2014] LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1). FORMULA G.f.: -24*x^2*(x+1)*(x^4+116*x^3+606*x^2+116*x+1)/(x-1)^9. [Colin Barker, Oct 11 2012] a(n) = 24 * A189345(n). [Joerg Arndt, Oct 12 2012] a(n) = n^2*(n^6 - 6*n^4 + 11*n^2 - 6). - Jon Perry, Nov 08 2014 a(0)=0, a(1)=0, a(2)=24, a(3)=3024, a(4)=43680, a(5)=303600, a(6)=1413720, a(7)=5085024, a(8)=15249024, a(n)=9*a(n-1)-36*a(n-2)+84*a(n-3)- 126*a(n-4)+ *a(n-5)-84*a(n-6)+36*a(n-7)-9*a(n-8)+a(n-9). - Harvey P. Dale, Mar 02 2015 EXAMPLE For n=3, there are 3024 such matrices, e.g. ((123),(400),(000)) and ((030),(140),(002)). MATHEMATICA Table[(n^2) (n^2 - 1) (n^2 - 2) (n^2 - 3), {n, 0, 30}] (* T. D. Noe, Oct 10 2012 *) CoefficientList[Series[-24 x^2 (x + 1) (x^4 + 116 x^3 + 606*x^2 + 116*x + 1)/(x-1)^9, {x, 0, 40}], x] (* Vincenzo Librandi, Oct 25 2014 *) Table[Times@@(n^2-Range[0, 3]), {n, 0, 30}] (* or *) LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {0, 0, 24, 3024, 43680, 303600, 1413720, 5085024, 15249024}, 30] (* Harvey P. Dale, Mar 02 2015 *) PROG (Maxima) makelist((n^2)*(n^2-1)*(n^2-2)*(n^2-3), n, 0, 25); /* Martin Ettl, Oct 11 2012 */ (PARI) a(n)=(n^2)*(n^2-1)*(n^2-2)*(n^2-3);  /* Joerg Arndt, Oct 12 2012 */ (MAGMA) [(n^2)*(n^2-1)*(n^2-2)*(n^2-3): n in [0..30]]; // Vincenzo Librandi, Oct 25 2014 CROSSREFS Sequence in context: A222852 A189246 A001512 * A272179 A088731 A299697 Adjacent sequences:  A217571 A217572 A217573 * A217575 A217576 A217577 KEYWORD nonn,easy AUTHOR Debashish Sharma, Oct 07 2012 STATUS approved

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Last modified May 20 01:04 EDT 2022. Contains 353847 sequences. (Running on oeis4.)