A204631 - OEIS

%I #41 Sep 08 2022 08:46:01

%S 1,1,2,3,5,7,11,17,26,40,62,96,148,229,354,547,845,1306,2018,3118,

%T 4818,7445,11504,17776,27468,42444,65585,101343,156597,241976,373905,

%U 577764,892770,1379522,2131659,3293873,5089744,7864752,12152738,18778601,29016988

%N Expansion of 1/(1 - x - x^2 + x^5 - x^7).

%C Limiting ratio is 1.5452156..., the real root of x^7 - x^6 - x^5 + x^2 - 1.

%H G. C. Greubel, <a href="/A204631/b204631.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,0,-1,0,1).

%F a(n) = a(n-1) + a(n-2) - a(n-5) + a(n-7). - _Franck Maminirina Ramaharo_, Nov 02 2018

%p seq(coeff(series(1/(1-x-x^2+x^5-x^7), x, n+1), x, n), n = 0..50); # _G. C. Greubel_, Mar 16 2020

%t CoefficientList[Series[1/(1 - x - x^2 + x^5 - x^7), {x, 0, 50}], x]

%t LinearRecurrence[{1,1,0,0,-1,0,1},{1,1,2,3,5,7,11},50] (* _Harvey P. Dale_, Aug 28 2013 *)

%o (PARI) my(x='x+O('x^50)); Vec(1/(1-x-x^2+x^5-x^7)) \\ _G. C. Greubel_, Nov 16 2016

%o (Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x-x^2+x^5-x^7))); // _G. C. Greubel_, Nov 03 2018

%Y Cf. A029826, A117791, A143419, A143438, A143472, A143619, A143644, A147663, A173908, A173911, A173924, A173925, A174522, A175740, A175772, A175773, A175782, A181600, A225391, A225393, A225394, A225482, A225499.

%K nonn,easy

%O 0,3

%A _Roger L. Bagula_, Jan 17 2012