A080610 Partial sums of Jacobsthal gap sequence.

0, 1, 4, 5, 20, 21, 84, 85, 340, 341, 1364, 1365, 5460, 5461, 21844, 21845, 87380, 87381, 349524, 349525, 1398100, 1398101, 5592404, 5592405, 22369620, 22369621, 89478484, 89478485, 357913940, 357913941, 1431655764, 1431655765, 5726623060

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Formula

a(2n-1) = A001045(2n) = A002450(n); a(2n) = A001045(2n) - 1 = A002450(n) - 1.

G.f.: x*(1+4*x)/((1-x^2)*(1-4x^2)). - Ralf Stephan, Sep 16 2003

a(n) = 2^n+(-2)^n/3-(-1)^n/2-5/6. - Paul Barry, Apr 22 2004

a(n) = a(n-1)*4 if n even; a(n) = a(n-1)+1 if n odd. - Philippe Deléham, Apr 22 2013

Mathematica

CoefficientList[Series[x (1 + 4 x) / ((1 - x^2) (1 - 4 x^2)), {x, 0, 40}], x] (* Vincenzo Librandi, Aug 05 2013 *)
LinearRecurrence[{0, 5, 0, -4}, {0, 1, 4, 5}, 40] (* Harvey P. Dale, Nov 11 2021 *)

Prog

(Magma) [2^n+(-2)^n/3-(-1)^n/2-5/6: n in [0..30]]; // Vincenzo Librandi, Aug 05 2013

Crossrefs

Cf. A075427, A080924, A094025.

Sequence in context: A099897 A050251 A125995 * A047175 A133632 A163141

Adjacent sequences: A080607 A080608 A080609 * A080611 A080612 A080613

Keyword

nonn,easy

Author

Paul Barry, Feb 26 2003

Status

approved