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 A074605 a(n) = 3^n + 4^n. 5
 2, 7, 25, 91, 337, 1267, 4825, 18571, 72097, 281827, 1107625, 4371451, 17308657, 68703187, 273218425, 1088090731, 4338014017, 17309009347, 69106897225, 276040168411, 1102998412177, 4408506864307, 17623567104025 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS x^n + y^n = (x+y)*a(n-1) - (x*y)*a(n-2). - Vincenzo Librandi, Jul 19 2010 REFERENCES L. B. W. Jolley, "Summation of Series", Dover Publications, 1961, p. 14. LINKS B. Berselli, Table of n, a(n) for n = 0..1000. - Bruno Berselli, Jul 20 2010 Index entries for linear recurrences with constant coefficients, signature (7,-12). FORMULA 2 + 7x + 25x^2 + 91x^3  + ... n terms = (1 - 4^n*x^n)/(1 - 4x) + (1 - 3^n*x^n)/(1 - 3x). [Jolley] - Gary W. Adamson, Dec 20 2006 From Mohammad K. Azarian, Jan 11 2009: (Start) G.f.: 1/(1-3*x) + 1/(1-4*x). E.g.f.: e^(3*x) + e^(4*x). (End) a(n) = 3*a(n-1) + 4^(n-1). - Bruno Berselli, Jul 20 2010 a(n) = 7*a(n-1) - 12*a(n-2) with a(0)=2, a(1)=7. - Vincenzo Librandi, Jul 19 2010 EXAMPLE a(2) = 7*7  - 12*2  =  25; a(3) = 7*25 - 12*7  =  91; a(4) = 7*91 - 12*25 = 337. MATHEMATICA Table[3^n + 4^n, {n, 0, 25}] PROG (PARI) a(n)=3^n+4^n \\ Charles R Greathouse IV, Oct 07 2015 CROSSREFS Cf. A000051, A034472, A052539, A034474, A062394, A034491, A062395, A062396, A007689, A063376, A063481, A074600..A074624. Equals A074506(n) - 1. Sequence in context: A108152 A024482 A097613 * A292613 A108081 A270785 Adjacent sequences:  A074602 A074603 A074604 * A074606 A074607 A074608 KEYWORD easy,nonn AUTHOR Robert G. Wilson v, Aug 25 2002 STATUS approved

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Last modified October 21 07:07 EDT 2019. Contains 328292 sequences. (Running on oeis4.)