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A052481
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a(n) = 2^n*(binomial(n,2) + 1).
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3
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1, 2, 8, 32, 112, 352, 1024, 2816, 7424, 18944, 47104, 114688, 274432, 647168, 1507328, 3473408, 7929856, 17956864, 40370176, 90177536, 200278016, 442499072, 973078528, 2130706432, 4647288832, 10099884032, 21877489664, 47244640256
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OFFSET
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0,2
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COMMENTS
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a(n) is the generalized Euler number of an (n+2)-dimensional hypercube: (number of vertices) - (number of edges) + (number of faces) = A000079(n+2) - A001787(n+2) + A001788(n+1). - Amiram Eldar, Nov 08 2019
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LINKS
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FORMULA
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For the sequence 1, 1, 1, 2, 8, 32, ... we have a(n) = 2^n*(n^2-5n+8)/8. - Paul Barry, Jun 26 2003
a(n) = 6*a(n-1) - 12*a(n-2) + 8*a(n-3).
G.f.: (1-4*x+8*x^2)/(1-2*x)^3. (End)
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MATHEMATICA
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LinearRecurrence[{6, -12, 8}, {1, 2, 8}, 30] (* Harvey P. Dale, May 16 2019 *)
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PROG
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(Sage) [2^(n-1)*(n^2-n+2) for n in (0..30)] # G. C. Greubel, May 16 2019
(GAP) List([0..30], n-> 2^(n-1)*(n^2-n+2)) # G. C. Greubel, May 16 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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