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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 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 22 09:59 EDT 2021. Contains 343174 sequences. (Running on oeis4.)