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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 (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)= 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 LINKS G. C. Greubel, Table of n, a(n) for n = 0..850 Index entries for linear recurrences with constant coefficients, signature (9,72). 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 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. = 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 Cf. A154929, A154996, A154997, A154999, A155000. 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 May 11 01:05 EDT 2021. Contains 343784 sequences. (Running on oeis4.)