cp's OEIS Frontend

A275761 G.f.: 1/(1 - x/(1+2*x - x^3/(1+2*x^2 - x^5/(1+2*x^3 - x^7/(1+2*x^4 - x^9/(1 - ...)))))), a continued fraction.

%I A275761 #19 Oct 30 2017 17:49:39
%S A275761 1,1,-1,1,0,-1,0,2,-1,-2,1,3,-3,-1,3,1,-7,3,7,-2,-12,10,5,-10,-8,27,
%T A275761 -8,-23,2,46,-38,-20,30,45,-100,27,71,12,-183,141,65,-71,-213,384,
%U A275761 -100,-202,-145,729,-545,-172,93,993,-1497,430,452,962,-2982,2188,250,451,-4527,6014,-2119,-296,-5456,12440,-9197,1206,-5307,20547,-24963,11156,-5513,28712,-53013,40590,-15529,36553,-93599,107065,-60129,52093,-145383,231326,-186656,113800,-214705,429584,-474454,323536
%N A275761 G.f.: 1/(1 - x/(1+2*x - x^3/(1+2*x^2 - x^5/(1+2*x^3 - x^7/(1+2*x^4 - x^9/(1 - ...)))))), a continued fraction.
%C A275761 Row sums of triangle A275760.
%C A275761 Limit a(n)/a(n+1) = -0.83683607462189175014302689979307768909437126147437...
%H A275761 Paul D. Hanna, <a href="/A275761/b275761.txt">Table of n, a(n) for n = 0..500</a>
%F A275761 G.f.: 1/(1 - x/(1+x + x/(1+x^2 - x^4/(1+x^3 + x^2/(1+x^4 - x^7/(1+x^5 + x^3/(1+x^6 - x^10/(1+x^7 + x^4/(1+x^8 - x^13/(1+x^9 + x^5/(1+x^10 - x^16/(1 + ...)))))))))))), a continued fraction.
%F A275761 G.f.: G(x,1) where G(x,y) = x*y + 1/G(x,x*y) with G(0,y) = 1 (cf. A275760).
%F A275761 G.f.: 1 + x/(1 + x/(1 + x^2/(1 + x^2/(1 + x^3/(1 + x^3/(1 + ...)))))). Cf. A006958 and A227309. - _Peter Bala_, Oct 29 2017
%e A275761 G.f.: A(x) = 1 + x - x^2 + x^3 - x^5 + 2*x^7 - x^8 - 2*x^9 + x^10 + 3*x^11 - 3*x^12 - x^13 + 3*x^14 + x^15 - 7*x^16 + 3*x^17 + 7*x^18 - 2*x^19 - 12*x^20 +...
%e A275761 such that
%e A275761 A(x) = 1/(1 - x/(1 + 2*x - x^3/(1 + 2*x^2 - x^5/(1 + 2*x^3 - x^7/(1 + 2*x^4 - x^9/(1 + 2*x^5 - x^11/(1 + 2*x^6 - x^13/(1 - ...)))))))).
%e A275761 RELATED SERIES.
%e A275761 1/A(x) = 1 - x + 2*x^2 - 4*x^3 + 7*x^4 - 12*x^5 + 22*x^6 - 41*x^7 + 74*x^8 - 133*x^9 + 243*x^10 - 444*x^11 + 806*x^12 - 1465*x^13 + 2669*x^14 - 4859*x^15 + 8840*x^16 - 16087*x^17 + 29282*x^18 - 53296*x^19 + 96994*x^20 - 176527*x^21 + 321290*x^22 - 584755*x^23 + 1064251*x^24 +...+ A275762(n)*x^n +...
%o A275761 (PARI) {a(n) = my(A=1 +x*O(x^n)); for(k=0, n, A = 1/A + y*x^(n+1-k)); subst(polcoeff(A, n),y,1)}
%o A275761 for(n=0,100,print1(a(n),", "))
%Y A275761 Cf. A275760, A275762, A006958, A227309.
%K A275761 sign
%O A275761 0,8
%A A275761 _Paul D. Hanna_, Aug 08 2016