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Partial sums of a Jacobsthal related sequence.
1

%I #24 Jan 29 2017 01:59:48

%S 0,1,2,7,10,31,42,127,170,511,682,2047,2730,8191,10922,32767,43690,

%T 131071,174762,524287,699050,2097151,2796202,8388607,11184810,

%U 33554431,44739242,134217727,178956970,536870911,715827882,2147483647,2863311530,8589934591

%N Partial sums of a Jacobsthal related sequence.

%C Partial sums of A084183.

%H Colin Barker, <a href="/A084184/b084184.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,5,0,-4).

%F G.f.: x*(1+2*x+2*x^2) / ((1-x^2)*(1-4*x^2)). - typo fixed by _Colin Barker_, Sep 09 2016

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

%F From _Colin Barker_, Sep 09 2016: (Start)

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

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

%F (End)

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

%t LinearRecurrence[{0,5,0,-4},{0,1,2,7},40] (* _Harvey P. Dale_, Jan 18 2015 *)

%o (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

%Y Cf. A001045, A002450, A083420, A084183.

%K easy,nonn

%O 0,3

%A _Paul Barry_, May 19 2003