A102901 a(n) = a(n-1) + 6*a(n-2), a(0)=1, a(1)=0.

1, 0, 6, 6, 42, 78, 330, 798, 2778, 7566, 24234, 69630, 215034, 632814, 1923018, 5719902, 17258010, 51577422, 155125482, 464590014, 1395342906, 4182882990, 12554940426, 37652238366, 112981880922, 338895311118, 1016786596650

Offset: 0

Author

Paul Barry, Jan 17 2005

Keywords

• easy
• nonn

Comments

Binomial transform is A102900.

Hankel transform is = 1,6,0,0,0,0,0,0,0,0,0,0,... - Philippe Deléham, Nov 02 2008

Examples

			a(6) = 330; (2*3^6 + 3*(-2)^6)/5 = (1458 + 192)/5 = 330.
		

References

• Maria Paola Bonacina and Nachum Dershowitz, Canonical Inference for Implicational Systems, in Automated Reasoning, Lecture Notes in Computer Science, Volume 5195/2008, Springer-Verlag.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,6).

Crossrefs

Cf. A015441, A102900.

Programs

Magma

[(2*3^n+3*(-2)^n)/5: n in [0..50]]; // Vincenzo Librandi, Jul 20 2013

Maple

A102901:=n->(2*3^n+3*(-2)^n)/5; seq(A102901(k), k=0..60); # Wesley Ivan Hurt, Nov 05 2013

Mathematica

CoefficientList[Series[(1-x)/((1+2x)(1-3x)), {x,0,50}], x] (* Vincenzo Librandi, Jul 20 2013 *)

PARI

a(n)=([0,1; 6,1]^n*[1;0])[1,1] \\ Charles R Greathouse IV, Mar 28 2016

SageMath

A102901=BinaryRecurrenceSequence(1,6,1,0)
[A102901(n) for n in range(51)] # G. C. Greubel, Dec 09 2022

Formula

G.f.: (1-x)/((1+2*x)*(1-3*x)).

a(n) = (2*3^n + 3*(-2)^n)/5.

a(n) = 6*A015441(n-1), for n>0.