A098890 a(n) = A001652(n)*A046090(n)+1 = A098602(n)+1.

1, 13, 421, 14281, 485113, 16479541, 559819261, 19017375313, 646030941361, 21946034630941, 745519146510613, 25325704946729881, 860328449042305321, 29225841562491651013, 992818284675673829101, 33726595837410418538401, 1145711440187278556476513

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..653

Index entries for linear recurrences with constant coefficients, signature (35,-35,1).

Formula

For n>0, a(n) = A001541(n)^2 + A001542(n)^2 - A098602(n-1).

G.f.: -(x^2-22*x+1) / ((x-1)*(x^2-34*x+1)). - Colin Barker, Jul 09 2015

a(n) = (5/8+1/16*(17+12*sqrt(2))^(-n)*(3-2*sqrt(2)+(3+2*sqrt(2))*(17+12*sqrt(2))^(2*n))). - Colin Barker, Mar 02 2016

Example

a(3) = 14281 = 99^2+70^2-420.

Prog

(PARI) Vec(-(x^2-22*x+1)/((x-1)*(x^2-34*x+1)) + O(x^30)) \\ Colin Barker, Jul 09 2015

Crossrefs

Cf. A001541, A001542, A001652, A046090, A098602.

Sequence in context: A142484 A087872 A308341 * A012023 A081442 A100872

Adjacent sequences: A098887 A098888 A098889 * A098891 A098892 A098893

Keyword

nonn,easy

Author

Charlie Marion, Nov 03 2004

Extensions

Name and a(0) corrected by Charlie Marion, Jul 09 2015

Status

approved