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A164545 a(n) = 4*a(n-1) + 4*a(n-2) for n > 1; a(0) = 1, a(1) = 8. 4
1, 8, 36, 176, 848, 4096, 19776, 95488, 461056, 2226176, 10748928, 51900416, 250597376, 1209991168, 5842354176, 28209381376, 136206942208, 657665294336, 3175488946176, 15332616962048, 74032423632896, 357460162379776 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A164544. Second binomial transform of A164640. Inverse binomial transform of A038761.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000 [extending from n(164) by Vincenzo Librandi]

Martin Burtscher, Igor Szczyrba, RafaƂ Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.

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

FORMULA

a(n) = 4*a(n-1) + 4*a(n-2) for n > 1; a(0) = 1, a(1) = 8.

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

G.f.: (1+4*x)/(1-4*x-4*x^2).

MATHEMATICA

LinearRecurrence[{4, 4}, {1, 8}, 30] (* Harvey P. Dale, Dec 25 2011 *)

PROG

(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((2+3*r)*(2+2*r)^n+(2-3*r)*(2-2*r)^n)/4: n in [0..21] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 19 2009

CROSSREFS

Cf. A164544, A164640, A038761.

Sequence in context: A055064 A014347 A200053 * A199310 A316107 A054627

Adjacent sequences:  A164542 A164543 A164544 * A164546 A164547 A164548

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 February 22 09:07 EST 2020. Contains 332133 sequences. (Running on oeis4.)