A120694 Sequence demonstrating the Pythagorean theorem.

1, 25, 1201, 58825, 2882401, 141237625, 6920643601, 339111536425, 16616465284801, 814206798955225, 39896133148806001, 1954910524291494025, 95790615690283207201, 4693740168823877152825, 229993268272369980488401, 11269670145346129043931625

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