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 A120694 Sequence demonstrating the Pythagorean theorem. 1
 1, 25, 1201, 58825, 2882401, 141237625, 6920643601, 339111536425, 16616465284801, 814206798955225, 39896133148806001, 1954910524291494025, 95790615690283207201, 4693740168823877152825, 229993268272369980488401, 11269670145346129043931625 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..500 Index entries for linear recurrences with constant coefficients, signature (50,-49). FORMULA sqrt((a(n)^2 - (a(n)-1)^2)) = 7^n. a(n) = 50*a(n-1) - 49*a(n-2). a(n) = (1/2)*(1 + 49^n). G.f.: (1-25*x)/(1-10*x+49*x^2). - Harvey P. Dale, Dec 31 2011 E.g.f.: (1/2)*(exp(x) + exp(49*x)). - G. C. Greubel, Dec 28 2022 MATHEMATICA LinearRecurrence[{50, -49}, {1, 25}, 21] (* Harvey P. Dale, Dec 31 2011 *) PROG (Magma) [(1+(49)^n)/2: n in [0..20]]; // G. C. Greubel, Dec 28 2022 (SageMath) [(1+(49)^n)/2 for n in range(21)] # G. C. Greubel, Dec 28 2022 CROSSREFS Sequence in context: A012508 A112102 A012799 * A012809 A014769 A012851 Adjacent sequences: A120691 A120692 A120693 * A120695 A120696 A120697 KEYWORD nonn AUTHOR Gary W. Adamson, Jun 28 2006 EXTENSIONS More terms from Harvey P. Dale, Dec 31 2011 STATUS approved

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Last modified July 16 12:01 EDT 2024. Contains 374348 sequences. (Running on oeis4.)