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

Author

Paul Barry, May 19 2003

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A001045, A002450, A083420, A084183.

Programs

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 *)

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

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)