A178906 a(n) = 111*a(n-1) - 100*a(n-2) with a(0)=0 and a(1)=1.

0, 1, 111, 12221, 1345431, 148120741, 16306859151, 1795249291661, 197641985459271, 21758735456812981, 2395455437160313791, 263719679979113532701, 29033338933965570750711, 3196328653672267000058821, 351889146664225079931458031, 38740062414361757172385959341, 4264958013327732538141695683751

Offset

0,3

Comments

Generalization of A001906.

Links

Table of n, a(n) for n=0..16.

Index entries for linear recurrences with constant coefficients, signature (111,-100).

Formula

a(n) = (1/11921)*sqrt(11921)*(((1/2)*(111+sqrt(11921)))^n - ((1/2)*(111-sqrt(11921)))^n), with n >= 0. - Paolo P. Lava, Aug 26 2010

G.f.: x / ( 1 - 111*x + 100*x^2 ). - R. J. Mathar, Aug 24 2011

Mathematica

Transpose[NestList[{#[[2]], 111#[[2]]-100#[[1]]}&, {0, 1}, 15]][[2]]  (* Harvey P. Dale, Jan 27 2011 *)

Crossrefs

Cf. A001906, A059317.

Sequence in context: A078270 A298677 A172175 * A225374 A015262 A201430

Adjacent sequences: A178903 A178904 A178905 * A178907 A178908 A178909

Keyword

nonn,easy

Author

Mark Dols, Jun 22 2010

Extensions

Corrected and extended by Harvey P. Dale, Jan 27 2011

Status

approved