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A080610 Partial sums of Jacobsthal gap sequence. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 2 19:59 EST 2022. Contains 358510 sequences. (Running on oeis4.)