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URL: https://oeis.org/A136302

⇱ A136302 - OEIS

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A136302
Transform of A000027 by the T_{1,1} transformation (see link).
9
2, 6, 15, 35, 81, 188, 437, 1016, 2362, 5491, 12765, 29675, 68986, 160373, 372822, 866706, 2014847, 4683951, 10888865, 25313540, 58846841, 136802308, 318026782, 739322571, 1718716457, 3995531011, 9288482690, 21593102505, 50197873146, 116695897118, 271285047567
OFFSET
1,1
FORMULA
G.f.: z*(2 + z^2)/(1 - 3*z + 2*z^2 - z^3).
a(n+3) = 3*a(n+2) - 2*a(n+1) + a(n) (n>=0). - Richard Choulet, Apr 07 2009
a(n) = 2*A095263(n) + A095263(n-2). - R. J. Mathar, Feb 29 2016
MAPLE
a:= n-> (<<6|2|1>>. <<3|1|0>, <-2|0|1>, <1|0|0>>^n)[1, 3]:
seq(a(n), n=1..40); # Alois P. Heinz, Aug 14 2008
MATHEMATICA
LinearRecurrence[{3, -2, 1}, {2, 6, 15}, 41] (* G. C. Greubel, Apr 12 2021 *)
PROG
(Magma) I:=[2, 6, 15]; [n le 3 select I[n] else 3*Self(n-1) -2*Self(n-2) +Self(n-3): n in [1..41]]; // G. C. Greubel, Apr 12 2021
(SageMath)
def A136302_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( x*(2+x^2)/(1-3*x+2*x^2-x^3) ).list()
a=A136302_list(41); a[1:] # G. C. Greubel, Apr 12 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Richard Choulet, Mar 22 2008
EXTENSIONS
More terms from Alois P. Heinz, Aug 14 2008
STATUS
approved