A112691 a(n) = J(n+1) mod J(n), J(n)=A001045(n).

1, 0, 0, 2, 1, 10, 1, 42, 1, 170, 1, 682, 1, 2730, 1, 10922, 1, 43690, 1, 174762, 1, 699050, 1, 2796202, 1, 11184810, 1, 44739242, 1, 178956970, 1, 715827882, 1, 2863311530, 1, 11453246122, 1, 45812984490, 1, 183251937962, 1, 733007751850, 1, 2932031007402

Offset

0,4

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,5,0,-4).

Formula

G.f.: x*(1-5*x^2+2*x^3+5*x^4-4*x^6) / (1-5*x^2+4*x^4).

a(2*n) = 1 - C(1, n) + C(0, n); a(2*n+1) = 2*A002450(n).

From Colin Barker, Apr 21 2017: (Start)

a(n) = (1 - (-2)^n + 5*(-1)^n + 2^n) / 6 for n>2.

a(n) = 5*a(n-2) - 4*a(n-4) for n>4.

(End)

Mathematica

LinearRecurrence[{0, 5, 0, -4}, {1, 0, 0, 2, 1, 10, 1}, 50] (* Harvey P. Dale, Oct 04 2018 *)

Prog

(PARI) Vec((1 - 5*x^2 + 2*x^3 + 5*x^4 - 4*x^6) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 + 2*x)) + O(x^30)) \\ Colin Barker, Apr 21 2017

Crossrefs

Sequence in context: A105606 A132995 A114692 * A110169 A144274 A144275

Adjacent sequences: A112688 A112689 A112690 * A112692 A112693 A112694

Keyword

easy,nonn

Author

Paul Barry, Sep 15 2005

Status

approved