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A155001 a(n) = 9*a(n-1) + 72*a(n-2), n > 2; a(0)=1, a(1)=1, a(2)=17. 2
1, 1, 17, 225, 3249, 45441, 642897, 9057825, 127809009, 1802444481, 25424248977, 358594243425, 5057894117169, 71339832581121, 1006226869666257, 14192509772837025, 200180922571503729, 2823489006787799361 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The sequences A155001, A155000, A154999, A154997 and A154996 have a common form: a(0)=a(1)=1, a(2)=2b+1, a(n)=(b+1)*a(n-1)+b(b+1)*a(n-2), with b some constant. The generating function of these is (1-b*x-b^2*x^2)/(1-(b+1)*x-b*(1+b)*x^2). - R. J. Mathar, Jan 20 2009

LINKS

Table of n, a(n) for n=0..17.

FORMULA

a(n+1) = Sum_{k=0..n} A154929(n,k)*8^(n-k).

a(n) = (1/2)*((9/2 + (3/2)*sqrt(41))^(n-1) + (9/2 - (3/2)*sqrt(41))^(n-1)) + (25/246)*sqrt(41)*((9/2 + (3/2)*sqrt(41))^(n-1) - (9/2 - (3/2)*sqrt(41))^(n-1) + (8/9)*(C(2*n,n) mod 2), n >= 0. - Paolo P. Lava, Jan 20 2009

MAPLE

a[0] := 1: a[1] := 1: a[2] := 17: for n from 3 to 25 do a[n] := 9*a[n-1]+72*a[n-2] end do: seq(a[n], n = 0 .. 17); # Emeric Deutsch, Jan 21 2009

MATHEMATICA

LinearRecurrence[{9, 72}, {1, 1, 17}, 20] (* Harvey P. Dale, Apr 26 2016 *)

CROSSREFS

Sequence in context: A181380 A081044 A016227 * A012095 A296999 A140842

Adjacent sequences:  A154998 A154999 A155000 * A155002 A155003 A155004

KEYWORD

nonn

AUTHOR

Philippe Deléham, Jan 18 2009

EXTENSIONS

Corrected by Philippe Deléham, Jan 21 2009

Corrected and extended by Emeric Deutsch and R. J. Mathar, Jan 21 2009

STATUS

approved

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Last modified April 26 04:11 EDT 2019. Contains 322469 sequences. (Running on oeis4.)