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

Author

Richard Choulet, Mar 22 2008

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A095263, A136303, A136304, A136305.

Programs

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

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 *)

Sage

def A136302_list(prec):
    P. = 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

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

Extensions

More terms from Alois P. Heinz, Aug 14 2008