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 A162667 a(n) = 20*a(n-1) - 97*a(n-2) for n > 1; a(0) = 1, a(1) = 10. 1
 1, 10, 103, 1090, 11809, 130450, 1463527, 16616890, 190375681, 2195675290, 25447064743, 295960791730, 3450850554529, 40308814292770, 471443782066087, 5518920654923050, 64648366238050561, 757632021233475370 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binomial transform of A152056. Tenth binomial transform of powers of 3 interleaved with zeros. LINKS G. C. Greubel, Table of n, a(n) for n = 0..930 Index entries for linear recurrences with constant coefficients, signature (20,-97). FORMULA a(n) = ((10+sqrt(3))^n + (10-sqrt(3))^n)/2. G.f.: (1-10*x)/(1-20*x+97*x^2). MAPLE seq(coeff(series((1-10*x)/(1-20*x+97*x^2), x, n+1), x, n), n = 0..20); # G. C. Greubel, Aug 27 2019 MATHEMATICA LinearRecurrence[{20, -97}, {1, 10}, 20] (* G. C. Greubel, Aug 27 2019 *) PROG (MAGMA) [ n le 2 select 9*n-8 else 20*Self(n-1)-97*Self(n-2): n in [1..18] ]; (PARI) my(x='x+O('x^20)); Vec((1-10*x)/(1-20*x+97*x^2)) \\ G. C. Greubel, Aug 27 2019 (Sage) def A162667_list(prec):     P. = PowerSeriesRing(ZZ, prec)     return P((1-10*x)/(1-20*x+97*x^2)).list() A162667_list(20) # G. C. Greubel, Aug 27 2019 (GAP) a:=[1, 10];; for n in [3..20] do a[n]:=20*a[n-1]-97*a[n-2]; od; a; # G. C. Greubel, Aug 27 2019 CROSSREFS Cf. A152056, A000244 (powers of 3). Sequence in context: A037596 A037687 A015588 * A027270 A227014 A036334 Adjacent sequences:  A162664 A162665 A162666 * A162668 A162669 A162670 KEYWORD nonn,easy AUTHOR Klaus Brockhaus, Jul 15 2009 STATUS approved

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Last modified April 19 21:57 EDT 2021. Contains 343117 sequences. (Running on oeis4.)