A117473 The values of 'a' in a^2 + b^2 = c^2, where b - a = 17 and gcd(a, b, c) = 1.

7, 28, 88, 207, 555, 1248, 3276, 7315, 19135, 42676, 111568, 248775, 650307, 1450008, 3790308, 8451307, 22091575, 49257868, 128759176, 287095935, 750463515, 1673317776, 4374021948, 9752810755, 25493668207

Offset

1,1

Comments

b - a = 17 is the third term in A058529.

Links

Table of n, a(n) for n=1..25.

Index entries for linear recurrences with constant coefficients, signature (1,6,-6,-1,1).

Formula

a(1) = 7, a(2) = 28, a(3) = 207, a(4) = 555, a(n) = 6*a(n-2) - a(n-4) + 34.

G.f.: x*(5*x^4 + 7*x^3 - 18*x^2 - 21*x - 7) / ((x-1)*(x^2 - 2*x - 1)*(x^2 + 2*x - 1)). - Colin Barker, Dec 17 2012

Example

a(5) = 6*88 - 7 + 34 = 555 and 555^2 + 572^2 = 797^2 and 572 - 555 = 17 and gcd(555, 572, 797) = 1.

Mathematica

CoefficientList[Series[(5x^4 + 7x^3 - 18x^2 - 21x - 7)/((x - 1)(x^2 - 2x - 1)(x^2 + 2x - 1)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Apr 14 2017 *)
LinearRecurrence[{1, 6, -6, -1, 1}, {7, 28, 88, 207, 555}, 30] (* Harvey P. Dale, Jul 31 2017 *)

Crossrefs

Cf. A058529, A117472.

Sequence in context: A054469 A369806 A156928 * A163037 A224153 A361771

Adjacent sequences: A117470 A117471 A117472 * A117474 A117475 A117476

Keyword

nonn,easy

Author

Andras Erszegi (erszegi.andras(AT)chello.hu), Mar 19 2006

Status

approved