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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
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
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.)