A136302 Transform of A000027 by the T_{1,1} transformation (see link).

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

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Richard Choulet, Curtz-like transformation.

Index entries for linear recurrences with constant coefficients, signature (3,-2,1).

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
(Sage)
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

Cf. A095263, A136303, A136304, A136305.

Sequence in context: A272340 A090982 A153517 * A116404 A301600 A084860

Adjacent sequences: A136299 A136300 A136301 * A136303 A136304 A136305

Keyword

nonn,easy

Author

Richard Choulet, Mar 22 2008

Extensions

More terms from Alois P. Heinz, Aug 14 2008

Status

approved