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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.
6
1, 1, 17, 225, 3249, 45441, 642897, 9057825, 127809009, 1802444481, 25424248977, 358594243425, 5057894117169, 71339832581121, 1006226869666257, 14192509772837025, 200180922571503729, 2823489006787799361
OFFSET
0,3
COMMENTS
The sequences A155001, A155000, A154999, A154997 and A154996 have a common form: a(0)=a(1)=1, a(2)= 2*b+1, a(n) = (b+1)*(a(n-1) + b*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
FORMULA
a(n+1) = Sum_{k=0..n} A154929(n,k)*8^(n-k).
G.f.: (1 - 8*x - 64*x^2)/(1 - 9*x - 72*x^2). - G. C. Greubel, Apr 20 2021
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 *)
PROG
(Magma) I:=[1, 17]; [1] cat [n le 2 select I[n] else 9*(Self(n-1) +8*Self(n-2)): n in [1..30]]; // G. C. Greubel, Apr 20 2021
(Sage)
def A155001_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1-8*x-64*x^2)/(1-9*x-72*x^2) ).list()
A155001_list(30) # G. C. Greubel, Apr 20 2021
CROSSREFS
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