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 A163346 a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 1, a(1) = 7. 4
 1, 7, 47, 309, 2009, 12983, 83623, 537621, 3452881, 22163527, 142219007, 912428949, 5853252329, 37546657463, 240841771063, 1544844588981, 9909085155361, 63559426007047, 407685301497167, 2614986216809589, 16773100233661049, 107586319349989943 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Binomial transform of A163350. Fifth binomial transform of A163403. LINKS Matthew House, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (10,-23). FORMULA a(n) = 10*a(n-1)-23*a(n-2) for n > 1; a(0) = 1, a(1) = 7. a(n) = ((1+sqrt(2))*(5+sqrt(2))^n + (1-sqrt(2))*(5-sqrt(2))^n)/2. G.f.: (1-3*x)/(1-10*x+23*x^2). E.g.f.: (sqrt(2)*sinh(sqrt(2)*x) + cosh(sqrt(2)*x))*exp(5*x). - Ilya Gutkovskiy, Jun 30 2016 MATHEMATICA CoefficientList[Series[(1 - 3 x)/(1 - 10 x + 23 x^2), {x, 0, 21}], x] (* Michael De Vlieger, Jun 30 2016 *) LinearRecurrence[{10, -23}, {1, 7}, 50] (* G. C. Greubel, Dec 19 2016 *) PROG (Magma) Z:=PolynomialRing(Integers()); N:=NumberField(x^2-2); S:=[ ((1+r)*(5+r)^n+(1-r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 26 2009 (PARI) Vec((1-3*x)/(1-10*x+23*x^2) + O(x^99)) \\ Altug Alkan, Jul 05 2016 CROSSREFS Cf. A163350, A163403. Sequence in context: A126635 A085352 A125370 * A186446 A244830 A126528 Adjacent sequences: A163343 A163344 A163345 * A163347 A163348 A163349 KEYWORD nonn,easy AUTHOR Al Hakanson (hawkuu(AT)gmail.com), Jul 25 2009 EXTENSIONS Edited and extended beyond a(5) by Klaus Brockhaus, Jul 26 2009 New name from G. C. Greubel, Dec 19 2016 STATUS approved

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Last modified January 29 00:02 EST 2023. Contains 359905 sequences. (Running on oeis4.)