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 A122946 a(0)=a(1)=0, a(2)=a(3)=2, for n>=3 a(n)=a(n-1)+4*a(n-3). 1
 0, 0, 2, 2, 2, 10, 18, 26, 66, 138, 242, 506, 1058, 2026, 4050, 8282, 16386, 32586, 65714, 131258, 261602, 524458, 1049490, 2095898, 4193730, 8391690, 16775282, 33550202, 67116962, 134218090, 268418898, 536886746, 1073759106, 2147434698 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS See lemma 5.2 of Reznick's preprint. LINKS Bruce Reznick, Regularity properties of the Stern enumeration of the rationals. Index entries for linear recurrences with constant coefficients, signature (1,0,4). FORMULA a(n)=(1/7)*2^(-2 + n/2)* (7*2^(n/2) - 7*Cos[n*(Pi - ArcTan[Sqrt[7]])] + 5*Sqrt[7]* Sin[n*(-Pi + ArcTan[Sqrt[7]])]) - Zak Seidov, Oct 26 2006 G.f.: -2*x^2 / ((2*x-1)*(2*x^2+x+1)). - Colin Barker, Jun 20 2013 PROG (PARI) a0=a1=0; a2=2; for(n=3, 50, a3=a2+4*a0; a0=a1; a1=a2; a2=a3; print1(a3, ", ")) CROSSREFS Cf. A002487. Sequence in context: A138674 A254706 A291666 * A087628 A263060 A089871 Adjacent sequences:  A122943 A122944 A122945 * A122947 A122948 A122949 KEYWORD nonn,easy AUTHOR Benoit Cloitre, Oct 24 2006 EXTENSIONS Entries checked by Zak Seidov, Oct 26 2006 STATUS approved

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Last modified December 1 20:54 EST 2020. Contains 338858 sequences. (Running on oeis4.)