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A163070 a(n) = ((4+sqrt(5))*(2+sqrt(5))^n + (4-sqrt(5))*(2-sqrt(5))^n)/2. 4
4, 13, 56, 237, 1004, 4253, 18016, 76317, 323284, 1369453, 5801096, 24573837, 104096444, 440959613, 1867934896, 7912699197, 33518731684, 141987625933, 601469235416, 2547864567597, 10792927505804, 45719574590813 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
Binomial transform of A163069. Second binomial transform of A163141. Inverse binomial transform of A163071.
LINKS
FORMULA
a(n) = 4*a(n-1) + a(n-2) for n > 1; a(0) = 4, a(1) = 13.
G.f.: (4-3*x)/(1-4*x-x^2).
a(n) = 2*A000032(3*n) + 5*A000045(3*n)/2 = 2*A014448(n) + 5*A001076(n). - Diego Rattaggi, Aug 09 2020
MATHEMATICA
LinearRecurrence[{4, 1}, {4, 13}, 30] (* Harvey P. Dale, Sep 19 2011 *)
PROG
(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-5); S:=[ ((4+r)*(2+r)^n+(4-r)*(2-r)^n)/2: n in [0..21] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 21 2009
(PARI) x='x+O('x^30); Vec((4-3*x)/(1-4*x-x^2)) \\ G. C. Greubel, Jan 08 2018
CROSSREFS
Sequence in context: A149476 A121076 A121070 * A239981 A243549 A344418
KEYWORD
nonn
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Jul 20 2009
EXTENSIONS
Edited and extended beyond a(5) by Klaus Brockhaus, Jul 21 2009
STATUS
approved

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Last modified June 19 09:37 EDT 2024. Contains 373501 sequences. (Running on oeis4.)