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 A133212 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3), n > 3; a(0) = 1, a(1) = 4, a(2) = 12, a(3) = 32. 2
 1, 4, 12, 32, 72, 144, 272, 512, 992, 1984, 4032, 8192, 16512, 33024, 65792, 131072, 261632, 523264, 1047552, 2097152, 4196352, 8392704, 16781312, 33554432, 67100672, 134201344, 268419072, 536870912, 1073774592, 2147549184 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Conjecture: a(n) = 2*A038503(n+3) if n > 0. - R. J. Mathar, Oct 23 2007 LINKS Table of n, a(n) for n=0..29. Index entries for linear recurrences with constant coefficients, signature (4,-6,4). FORMULA Sequence is identical to its fourth differences. From R. J. Mathar, Nov 18 2007: (Start) G.f.: -(1 + 2*x^2 + 4*x^3)/((2*x - 1)*(2*x^2 - 2*x + 1)). - [Corrected by Georg Fischer, May 12 2019] a(n) = -2*(-1)^n*A009116(n)+3*2^n. (End) E.g.f.: exp(x)*(3*cosh(x) - 2*(cos(x) + sin(x)) + 5*sinh(x)). - Stefano Spezia, Jan 03 2023 MAPLE A133212 := proc(n) option remember ; if n <= 3 then op(n+1, [1, 4, 12, 32]) ; else 4*A133212(n-1)-6*A133212(n-2)+4*A133212(n-3) ; fi ; end: seq(A133212(n), n=0..50) ; # R. J. Mathar, Oct 23 2007 MATHEMATICA Join[{1}, LinearRecurrence[{4, -6, 4}, {4, 12, 32}, 29]] (* Ray Chandler, Sep 23 2015 *) CROSSREFS Cf. A009116, A038503, A099087. Sequence in context: A233458 A335687 A348864 * A233447 A127811 A361099 Adjacent sequences: A133209 A133210 A133211 * A133213 A133214 A133215 KEYWORD nonn,easy AUTHOR Paul Curtz, Oct 11 2007 EXTENSIONS More terms from R. J. Mathar, Oct 23 2007 STATUS approved

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Last modified June 10 17:04 EDT 2023. Contains 363205 sequences. (Running on oeis4.)