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A109975 Second differences of A045623, prefixed by an initial 1. 3
1, 2, 4, 9, 20, 44, 96, 208, 448, 960, 2048, 4352, 9216, 19456, 40960, 86016, 180224, 376832, 786432, 1638400, 3407872, 7077888, 14680064, 30408704, 62914560, 130023424, 268435456, 553648128, 1140850688, 2348810240 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of [1,1,1,2,1,3,1,...]. [From Paul Barry, Mar 18 2009]

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-4).

FORMULA

G.f.: (1-2x+x^3)/(1-2x)^2. [From Paul Barry, Mar 18 2009]

a(n) = 2^(n-3)*(n+6) with n>1, a(0)=1, a(1)=2 (see the PARI code). - Bruno Berselli, Jun 27 2012

G.f.: Q(0)/(1-x), where Q(k)= 1 + (k+1)*x/(1 - x - x*(1-x)/(x + (k+1)*(1-x)/Q(k+1))); (continued fraction). - Sergei N. Gladkovskii, Apr 25 2013

MATHEMATICA

CoefficientList[Series[(1-2x+x^3)/(1-2x)^2, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 27 2012 *)

PROG

(PARI) a(n)=(n+6)<<(n-3)+(n<2) \\ Charles R Greathouse IV, Jun 01 2011

(MAGMA) I:=[1, 2, 4, 9]; [n le 4 select I[n] else 4*Self(n-1)-4*Self(n-2): n in [1..40]]; // Vincenzo Librandi, Jun 27 2012

CROSSREFS

Essentially a duplicate of A034007.

Sequence in context: A179744 A266930 A034007 * A129891 A130587 A129988

Adjacent sequences:  A109972 A109973 A109974 * A109976 A109977 A109978

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Jun 07 2007

STATUS

approved

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Last modified August 25 16:17 EDT 2019. Contains 326324 sequences. (Running on oeis4.)