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 A147958 a(n) = ((7 + sqrt(2))^n + (7 - sqrt(2))^n)/2. 4
 1, 7, 51, 385, 2993, 23807, 192627, 1577849, 13036417, 108350935, 904201491, 7566326929, 63431106929, 532418131343, 4472591813139, 37592633210825, 316085049734017, 2658336935367463, 22360719757645683, 188108240644768801 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 7th binomial transform of A077957. Binomial transform of A147957. Inverse binomial transform of A147959. - Philippe Deléham, Nov 30 2008 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (14, -47). FORMULA From Philippe Deléham, Nov 19 2008: (Start) a(n) = 14*a(n-1) - 47*a(n-2), n > 1; a(0)=1, a(1)=7. G.f.: (1 - 7*x)/(1 - 14*x + 47*x^2). a(n) = (Sum_{k=0..n} A098158(n,k)*7^(2k)*2^(n-k))/7^n. (End) E.g.f.: exp(7*x)*cosh(sqrt(2)*x). - Ilya Gutkovskiy, Aug 11 2017 MATHEMATICA LinearRecurrence[{14, -47}, {1, 7}, 50] (* G. C. Greubel, Aug 17 2018 *) PROG (Magma) Z:= PolynomialRing(Integers()); N:=NumberField(x^2-2); S:=[ ((7+r2)^n+(7-r2)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Nov 19 2008 (PARI) x='x+O('x^30); Vec((1-7*x)/(1-14*x+47*x^2)) \\ G. C. Greubel, Aug 17 2018 CROSSREFS Cf. A077957, A098158, A147957, A147959. Sequence in context: A137382 A162757 A285880 * A104454 A332936 A222849 Adjacent sequences: A147955 A147956 A147957 * A147959 A147960 A147961 KEYWORD nonn AUTHOR Al Hakanson (hawkuu(AT)gmail.com), Nov 17 2008 EXTENSIONS Extended beyond a(6) by Klaus Brockhaus, Nov 19 2008 STATUS approved

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Last modified September 7 05:42 EDT 2024. Contains 375729 sequences. (Running on oeis4.)