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 A162557 a(n) = ((3+sqrt(3))*(4+sqrt(3))^n+(3-sqrt(3))*(4-sqrt(3))^n)/6. 2
 1, 5, 27, 151, 857, 4893, 28003, 160415, 919281, 5268853, 30200171, 173106279, 992248009, 5687602445, 32601595443, 186873931759, 1071170713313, 6140004593637, 35194817476027, 201738480090935, 1156375213539129, 6628401467130877, 37994333961038339, 217785452615605311 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binomial transform of A086405. Inverse binomial transform of A162558. 4th binomial transform of A108411. 2nd binomial transform of A079935. [R. J. Mathar, Jul 17 2009] From J. Conrad, Aug 29 2016: (Start) Partial sum of A136777. Backward difference of Sum_{k=0..n} A027907(n+1,2k+2)*3^k. (End) String length in substitution system {0 -> 1001001, 1 -> 11011} at step n from initial string "1" (1 -> 11011 -> 110111101110010011101111011 -> ...). - Ilya Gutkovskiy, Aug 30 2016 LINKS Index entries for linear recurrences with constant coefficients, signature (8,-13). FORMULA a(n) = 8*a(n-1)-13*a(n-2) for n > 1; a(0) = 1, a(1) = 5. G.f.: (1-3*x)/(1-8*x+13*x^2). MAPLE seq(simplify(((3+sqrt(3))*(4+sqrt(3))^n+(3-sqrt(3))*(4-sqrt(3))^n)*1/6), n = 0..20); # Emeric Deutsch, Jul 14 2009 MATHEMATICA Table[FullSimplify[((3 + #) (4 + #)^n + (3 - #) (4 - #)^n)/6 &@ Sqrt@ 3], {n, 0, 23}] (* Michael De Vlieger, Aug 30 2016 *) PROG (MAGMA) Z:=PolynomialRing(Integers()); N:=NumberField(x^2-3); S:=[ ((3+r)*(4+r)^n+(3-r)*(4-r)^n)/6: n in [0..20] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 13 2009 (MAGMA) I:=[1, 5]; [n le 2 select I[n]  else 8*Self(n-1)-13*Self(n-2): n in [1..40]]; // Vincenzo Librandi, Aug 30 2016 CROSSREFS Cf. A108411 (powers of 3 repeated), A086405, A162558. Cf. A162558. [R. J. Mathar, Jul 17 2009] Sequence in context: A026292 A100193 A158869 * A134425 A305573 A184702 Adjacent sequences:  A162554 A162555 A162556 * A162558 A162559 A162560 KEYWORD nonn AUTHOR Al Hakanson (hawkuu(AT)gmail.com), Jul 06 2009 EXTENSIONS Edited, corrected and extended beyond a(5) by Klaus Brockhaus, Emeric Deutsch and R. J. Mathar, Jul 07 2009 More terms from Vincenzo Librandi, Aug 30 2016 STATUS approved

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Last modified January 16 21:37 EST 2019. Contains 319206 sequences. (Running on oeis4.)