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 A280059 Number of 2 X 2 matrices having all elements in {-n,..,0,..,n} with determinant = permanent. 2
 1, 45, 225, 637, 1377, 2541, 4225, 6525, 9537, 13357, 18081, 23805, 30625, 38637, 47937, 58621, 70785, 84525, 99937, 117117, 136161, 157165, 180225, 205437, 232897, 262701, 294945, 329725, 367137, 407277, 450241, 496125 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Indranil Ghosh, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA a(n) = 16*(n+1)^3 - 28*(n+1)^2 + 16*(n+1) - 3 for n>0. From G. C. Greubel, Dec 25 2016: (Start) G.f.: (1 + 41*x + 51*x^2 + 3*x^3)/(1 - x)^4. E.g.f.: (1 + 44*x + 68*x^2 + 16*x^3)*exp(x). a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End) MATHEMATICA Table[16*(n+1)^3 - 28*(n+1)^2 + 16*(n+1) - 3, {n, 0, 50}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 45, 225, 637}, 50] (* G. C. Greubel, Dec 25 2016 *) PROG def t(n): s=0 for a in range(-n, n+1): for b in range(-n, n+1): for c in range(-n, n+1): for d in range(-n, n+1): if (a*d-b*c)==(a*d+b*c): s+=1 return s for i in range(0, 1001): print str(i)+" "+str(t(i)) (PARI) for(n=0, 50, print1(16*(n+1)^3 - 28*(n+1)^2 + 16*(n+1) - 3, ", ")) \\ G. C. Greubel, Dec 25 2016 CROSSREFS Cf. A210000. Sequence in context: A203835 A087442 A334035 * A251451 A251444 A169717 Adjacent sequences: A280056 A280057 A280058 * A280060 A280061 A280062 KEYWORD nonn,easy AUTHOR Indranil Ghosh, Dec 25 2016 STATUS approved

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Last modified October 4 19:37 EDT 2023. Contains 365888 sequences. (Running on oeis4.)