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A189735 a(1)=3,  a(2)=1, a(n)=3*a(n-1) + a(n-2) 13
3, 1, 6, 19, 63, 208, 687, 2269, 7494, 24751, 81747, 269992, 891723, 2945161, 9727206, 32126779, 106107543, 350449408, 1157455767, 3822816709, 12625905894, 41700534391, 137727509067, 454883061592, 1502376693843, 4962013143121, 16388416123206, 54127261512739 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..100

Index entries for linear recurrences with constant coefficients, signature (3,1).

FORMULA

a(n)=3/2*((3/2-1 /2*sqrt(13))^(n-1)+(3/2+1/2*sqrt(13))^(n-1))+7/26*sqrt(13)*((3/2-1/2*sqrt(13))^(n-1)-(3/2+1/2*sqrt(13))^(n-1)), Paolo P. Lava, May 24 2011

G.f.: x*(3-8*x)/(1-3*x-x^2)  - Bruno Berselli, May 24 2011

MATHEMATICA

LinearRecurrence[{3, 1}, {3, 1}, 40]

PROG

(Maxima) a[1]:3$ a[2]:1$ a[n]:=3*a[n-1]+a[n-2]$ makelist(a[n], n, 1, 28);  [Bruno Berselli, May 24 2011]

(PARI) v=vector(99); v[1]=3; v[2]=1; for(i=3, #v, v[i]=3*v[i-1]+v[i-2]); v \\ Charles R Greathouse IV, May 24, 2011

CROSSREFS

Sequence in context: A100232 A221937 A333652 * A221693 A271969 A175291

Adjacent sequences:  A189732 A189733 A189734 * A189736 A189737 A189738

KEYWORD

nonn,easy

AUTHOR

Harvey P. Dale, Apr 26 2011

STATUS

approved

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Last modified April 14 22:47 EDT 2021. Contains 342971 sequences. (Running on oeis4.)