A178869 - OEIS

A178869

a(n) = 9*a(n-1) - 10*a(n-2); a(0)=0, a(1)=1.

0, 1, 9, 71, 549, 4231, 32589, 250991, 1933029, 14887351, 114655869, 883029311, 6800705109, 52376052871, 403377424749, 3106636294031, 23925952398789, 184267208648791, 1419145353851229, 10929636098173151, 84175271345046069

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OFFSET

0,3

COMMENTS

Alternating row sums of triangle A206819. Large Schroeder numbers in decimal expansion of ratio a(n)/a(n+1). [A-number corrected by Philippe Deléham, Feb 26 2013]

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (9, -10).

FORMULA

G.f.: -x/(-10*x^2+9*x-1).

a(n) = 9a(n-1)-10a(n-2), a(0)=0, a(1)=1. [Harvey P. Dale, May 06 2011]

a(n+1) = Sum_{k, 0<=k<=n}A206819(n,k)*(-1)^k. - Philippe Deléham, Feb 26 2013

MATHEMATICA

Join[{a=0, b=1}, Table[c=9*b-10*a+2; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Jan 20 2011 *)

LinearRecurrence[{9, -10}, {0, 1}, 50] (* or *) CoefficientList[Series[ -x/(-10x^2+9x-1), {x, 0, 50}], x] (* Harvey P. Dale, May 06 2011 *)

CROSSREFS

Cf. A006318, A171415, A104562, A206819.