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A164608 Expansion of (1+4*x)/(1-8*x+8*x^2). 3
1, 12, 88, 608, 4160, 28416, 194048, 1325056, 9048064, 61784064, 421888000, 2880831488, 19671547904, 134325731328, 917233467392, 6263261888512, 42768227368960, 292039723843584, 1994171971796992, 13617057983627264 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A054490. Fourth binomial transform of A164683. Inverse binomial transform of A164609.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..149

Index entries for linear recurrences with constant coefficients, signature (8,-8).

FORMULA

a(n) = 8*a(n-1)-8*a(n-2) for n > 1; a(0) = 1, a(1) = 12.

a(n) = A057084(n) + 4*A057084(n-1).

a(n) = ((2+4*sqrt(2))*(4+2*sqrt(2))^n+(2-4*sqrt(2))*(4-2*sqrt(2))^n)/4.

PROG

(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((2+4*r)*(4+2*r)^n+(2-4*r)*(4-2*r)^n)/4: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus, Aug 22 2009]

CROSSREFS

Cf. A054490, A164683, A164609.

Sequence in context: A178257 A057406 A125349 * A081009 A155635 A126507

Adjacent sequences:  A164605 A164606 A164607 * A164609 A164610 A164611

KEYWORD

nonn,easy

AUTHOR

Al Hakanson (hawkuu(AT)gmail.com), Aug 17 2009

EXTENSIONS

Edited and extended beyond a(5) by Klaus Brockhaus, Aug 22 2009

STATUS

approved

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Last modified December 9 00:45 EST 2016. Contains 278959 sequences.