A227376 - OEIS

%I #13 May 23 2021 02:56:32

%S 1,1,2,4,7,12,21,36,62,106,181,309,527,898,1530,2606,4438,7557,12867,

%T 21907,37297,63497,108100,184032,313298,533359,907988,1545751,2631469,

%U 4479778,7626309,12982911,22101900,37625912,64053725,109043981,185634620,316021206,537989084,915863373

%N G.f.: 1/(1 - x - x^2 - x^3 + x^5 + x^6 + x^7).

%C Compare to sequence A227375, generated by a continued fraction.

%C Lim_{n->infinity} a(n)/a(n+1) = 0.587411973105598587998520092901249815195963...

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

%F a(n) = a(n-1) + a(n-2) + a(n-3) - a(n-5) - a(n-6) - a(n-7). - _Wesley Ivan Hurt_, May 22 2021

%e G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 3*x^4 + 5*x^5 + 9*x^6 + 14*x^7 + 24*x^8 + ...

%t CoefficientList[Series[1/(1-x-x^2-x^3+x^5+x^6+x^7),{x,0,50}],x] (* _Harvey P. Dale_, Mar 09 2021 *)

%o (PARI) {a(n)=polcoeff(1/(1 - x - x^2 - x^3 + x^5 + x^6 + x^7 +x*O(x^n)),n)}

%o for(n=0,50,print1(a(n),", "))

%Y Cf. A227375.

%K nonn,easy

%O 0,3

%A _Paul D. Hanna_, Jul 09 2013