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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

Table of n, a(n) for n=0..33.

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: A284563 A138674 A254706 * 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 June 27 11:25 EDT 2017. Contains 288788 sequences.