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 A288486 Square rings obtained by adding four identical cuboids from A169938, a(n) = 4*n*(n+1)*(n*(n+1)+1). 3
 0, 24, 168, 624, 1680, 3720, 7224, 12768, 21024, 32760, 48840, 70224, 97968, 133224, 177240, 231360, 297024, 375768, 469224, 579120, 707280, 855624, 1026168, 1221024, 1442400, 1692600, 1974024, 2289168, 2640624, 3031080, 3463320, 3940224, 4464768, 5040024 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS If we fill the empty space with A288487(n) cubes, we get a solid cuboid with (n+1)^5 cubes (A000584(n+1)). LINKS Daniel Poveda Parrilla, Table of n, a(n) for n = 0..10000 Daniel Poveda Parrilla, Illustration of initial terms Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). FORMULA G.f.: 24*(x + 2*x^2 + x^3) / (1 - x)^5. a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). a(n) = A007204(n) - 1 = (A001844(n))^2 - 1. a(n) = 4*A169938(n) = 4*A002378(n)*A002061(n+1) = A033996(n)*A002061(n+1). MATHEMATICA Table[4 n (n + 1) (n^2 + n + 1), {n, 0, 28}] (* or *) CoefficientList[Series[24 (x + 2 x^2 + x^3)/(1 - x)^5, {x, 0, 28}], x] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {0, 24, 168, 624, 1680}, 29] PROG (PARI) Vec(24*(x + 2*x^2 + x^3)/(1 - x)^5 + O(x^28)) CROSSREFS Cf. A000584, A001844, A002061, A002378, A007204, A033996, A169938, A288487. Sequence in context: A019583 A244908 A087887 * A223291 A221069 A272125 Adjacent sequences: A288483 A288484 A288485 * A288487 A288488 A288489 KEYWORD nonn,easy AUTHOR Daniel Poveda Parrilla, Jun 10 2017 STATUS approved

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Last modified September 11 23:47 EDT 2024. Contains 375842 sequences. (Running on oeis4.)