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 A188570 Coefficients of the absolute term in (1 + sqrt(2) + sqrt(3))^n sequence, denoted as C1(n). 4
 1, 1, 6, 16, 80, 296, 1296, 5216, 21952, 90304, 375936, 1555456, 6456320, 26754560, 110963712, 460015616, 1907494912, 7908659200, 32792076288, 135963148288, 563742310400, 2337417887744, 9691567030272, 40183767891968, 166612591968256, 690819710058496 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 Index entries for linear recurrences with constant coefficients, signature (4,4,-16,8). FORMULA Recurrence: a(n) = 4*a(n-1) + 4*a(n-2) - 16*a(n-3) + 8*a(n-4). - Vaclav Kotesovec, Aug 13 2013 a(n) ~ (1+sqrt(3)+sqrt(2))^n/4. - Vaclav Kotesovec, Aug 13 2013 EXAMPLE C1(3) is equal to 16, because (1+sqrt(2)+sqrt(3))^3 = 16 + 14*sqrt(2) + 12*sqrt(3) + 6*sqrt(6). MATHEMATICA C1[n_] := Sum[Sum[2^(Floor[n/2] - k - j) 3^j Multinomial[2 k + n - 2 Floor[n/2], 2 j, 2 Floor[n/2] - 2 k - 2 j], {j, 0, Floor[n/2] - k}], {k, 0, Floor[n/2]}]; Table[C1[n], {n, 0, 25}] a[n_] := Expand[(1 + Sqrt[2] + Sqrt[3])^n] /. Sqrt[_] -> 0; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Jan 08 2013 *) LinearRecurrence[{4, 4, -16, 8}, {1, 1, 6, 16}, 30] (* Harvey P. Dale, Jan 25 2019 *) CROSSREFS Cf. A188571, A188572, A188573. Sequence in context: A350649 A211954 A230942 * A009352 A056204 A091148 Adjacent sequences: A188567 A188568 A188569 * A188571 A188572 A188573 KEYWORD nonn AUTHOR Mateusz Szymański, Dec 28 2012 STATUS approved

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Last modified August 7 20:39 EDT 2024. Contains 375017 sequences. (Running on oeis4.)