A155611 6^n - 3^n + 1.

1, 4, 28, 190, 1216, 7534, 45928, 277750, 1673056, 10058014, 60407128, 362619910, 2176250896, 13059099694, 78359381128, 470170635670, 2821066860736, 16926530304574, 101559569247928, 609358577749030, 3656154953278576

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Index entries for linear recurrences with constant coefficients, signature (10,-27,18).

Formula

G.f.: 1/(1-6*x)-1/(1-3*x)+1/(1-x). E.g.f.: e^(6*x)-e^(3*x)+e^x.

a(n)=9*a(n-1)-18*a(n-2)+10 with a(0)=1, a(1)=4 [From Vincenzo Librandi, Jul 21 2010]

E.g.f.: exp(6*x)-exp(3*x)+exp(x)= G(0) ; G(k)= 1 - 1/( 2^k + 2^k/( 3^k - 1 - 6*x*18^k/( x*6^(k+1)+(k+1)/G(k+1)))); (continued fraction, 3-step ). - Sergei N. Gladkovskii, Jan 10 2012

Prog

(PARI) a(n)=6^n-3^n+1 \\ Charles R Greathouse IV, Jan 09 2012

Crossrefs

Cf. A155596-A155610.

Sequence in context: A366810 A219405 A001396 * A218175 A002903 A208704

Adjacent sequences: A155608 A155609 A155610 * A155612 A155613 A155614

Keyword

nonn,easy

Author

Mohammad K. Azarian, Jan 26 2009

Status

approved