A084184 Partial sums of a Jacobsthal related sequence.

0, 1, 2, 7, 10, 31, 42, 127, 170, 511, 682, 2047, 2730, 8191, 10922, 32767, 43690, 131071, 174762, 524287, 699050, 2097151, 2796202, 8388607, 11184810, 33554431, 44739242, 134217727, 178956970, 536870911, 715827882, 2147483647, 2863311530, 8589934591

Offset

0,3

Comments

Partial sums of A084183.

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+2*x+2*x^2) / ((1-x^2)*(1-4*x^2)). - typo fixed by Colin Barker, Sep 09 2016

a(2*n+1) = A083420(n). a(2*n) = 2*A002450(n) = 2*A001045(2*n).

From Colin Barker, Sep 09 2016: (Start)

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

a(n) = 5*a(n-2) - 4*a(n-4) for n>3.

(End)

Maple

A084184:=n->(5-(-1)^n)*(2^n-1)/6: seq(A084184(n), n=0..50); # Wesley Ivan Hurt, Jan 28 2017

Mathematica

LinearRecurrence[{0, 5, 0, -4}, {0, 1, 2, 7}, 40] (* Harvey P. Dale, Jan 18 2015 *)

Prog

(PARI) concat(0, Vec(x*(1+2*x+2*x^2)/((1-x^2)*(1-4*x^2)) + O(x^40))) \\ Colin Barker, Sep 09 2016

Crossrefs

Cf. A001045, A002450, A083420, A084183.

Sequence in context: A091295 A361931 A215407 * A015963 A293002 A056656

Adjacent sequences: A084181 A084182 A084183 * A084185 A084186 A084187

Keyword

easy,nonn

Author

Paul Barry, May 19 2003

Status

approved