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A275761
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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.
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4
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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, -8, -23, 2, 46, -38, -20, 30, 45, -100, 27, 71, 12, -183, 141, 65, -71, -213, 384, -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
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OFFSET
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0,8
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COMMENTS
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Limit a(n)/a(n+1) = -0.83683607462189175014302689979307768909437126147437...
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LINKS
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FORMULA
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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.
G.f.: G(x,1) where G(x,y) = x*y + 1/G(x,x*y) with G(0,y) = 1 (cf. A275760).
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
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EXAMPLE
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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 +...
such that
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 - ...)))))))).
RELATED SERIES.
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 +...
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PROG
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(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)}
for(n=0, 100, print1(a(n), ", "))
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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