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A164546 a(n) = 8*a(n-1)-8*a(n-2) for n > 1; a(0) = 1, a(1) = 10. 4
1, 10, 72, 496, 3392, 23168, 158208, 1080320, 7376896, 50372608, 343965696, 2348744704, 16038232064, 109515898880, 747821334528, 5106443485184, 34868977205248, 238100269760512, 1625850340442112, 11102000565452800 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A038761. Fourth binomial transform of A164640. Inverse binomial transform of A164547.

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) = 10.

a(n) = ((2+3*sqrt(2))*(4+2*sqrt(2))^n + (2-3*sqrt(2))*(4-2*sqrt(2))^n)/4.

G.f.: (1+2*x)/(1-8*x+8*x^2).

PROG

(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((2+3*r)*(4+2*r)^n+(2-3*r)*(4-2*r)^n)/4: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 19 2009

CROSSREFS

Cf. A038761, A164640, A164547.

Sequence in context: A264159 A228316 A228310 * A221552 A037712 A037614

Adjacent sequences:  A164543 A164544 A164545 * A164547 A164548 A164549

KEYWORD

nonn,easy

AUTHOR

Al Hakanson (hawkuu(AT)gmail.com), Aug 15 2009

EXTENSIONS

Edited and extended beyond a(5) by Klaus Brockhaus, Aug 19 2009

STATUS

approved

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Last modified April 19 08:26 EDT 2021. Contains 343110 sequences. (Running on oeis4.)