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 A093406 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) + a(n-4). 2
 1, 3, 11, 31, 71, 145, 289, 601, 1321, 2979, 6683, 14743, 32111, 69697, 151777, 332113, 728689, 1598883, 3503627, 7668079, 16774775, 36704017, 80343361, 175916521, 385196761, 843365379, 1846290395, 4041672871, 8847607391, 19368919297, 42403014721, 92830645537 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n)/a(n-1) tends to 2.189207115... = 1 + 2^(1/4) = 1 + A010767. REFERENCES E. J. Barbeau, Polynomials, Springer-Verlag NY Inc, 1989, p. 136. LINKS Index entries for linear recurrences with constant coefficients, signature (4,-6,4,1). FORMULA We use a 4 X 4 matrix corresponding to the characteristic polynomial (x - 1)^4 - 2 = 0 = x^4 - 4x^3 + 6x^2 - 4x - 1 = 0, being [0 1 0 0 / 0 0 1 0 / 0 0 0 1 / 1 4 -6 4]. Let the matrix = M. Perform M^n * [1, 1, 1, 1]. a(n) = the third term from the left, (the other 3 terms being offset members of the series). a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)+a(n-4). G.f.: -x*(x^3+5*x^2-x+1)/ (x^4+4*x^3-6*x^2+4*x-1). [Colin Barker, Oct 21 2012] EXAMPLE a(4) = 31, since M^4 * [1,1,1,1] = [3, 11, 31, 71]. MATHEMATICA LinearRecurrence[{4, -6, 4, 1}, {1, 3, 11, 31}, 40] (* Harvey P. Dale, Jul 22 2013 *) CROSSREFS Cf. A010767, A052101. Sequence in context: A261148 A071568 A097081 * A107587 A245931 A190590 Adjacent sequences:  A093403 A093404 A093405 * A093407 A093408 A093409 KEYWORD nonn,easy AUTHOR Gary W. Adamson, Mar 28 2004 EXTENSIONS Corrected by T. D. Noe, Nov 08 2006 New name using recurrence from Colin Barker, Joerg Arndt, Apr 15 2021 STATUS approved

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Last modified July 28 07:13 EDT 2021. Contains 346317 sequences. (Running on oeis4.)