A213411 -id:A213411 - cp's OEIS frontend

A291419 G.f. A(x) = Sum_{n>=0} a(n)x^n satisfies A(x) = 1/(1 - a(0)x^a(0)/(1 - a(1)x^a(1)/(1 - a(2)x^a(2)/(1 - ...)))), a continued fraction.

1, 1, 2, 4, 10, 24, 60, 148, 376, 944, 2392, 6032, 15280, 38608, 97728, 247104, 625312, 1581568, 4001680, 10122624, 25610368, 64787520, 163907904, 414654848, 1049031104, 2653873152, 6713958912, 16985280000, 42970438432, 108708830336, 275018076928, 695755635328, 1760162851328

Offset: 0

Ilya Gutkovskiy, Aug 23 2017

nonn

			G.f. = 1 + x + 2*x^2 + 4*x^3 + 10*x^4 + 24*x^5 + 60*x^6 + ... = 1/(1 - x/(1 - x/(1 - 2*x^2/(1 - 4*x^4/(1 - 10*x^10/(1 - ...)))))).

Cf. A213411, A213435.

A293855 G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies A(x) = 1/(1 - x^a(1) - x^a(2)/(1 - x^a(3) - x^a(4)/(1 - x^a(5) - x^a(6)/(1 - ... )))), a continued fraction.

Original entry on oeis.org

1, 1, 2, 3, 5, 9, 15, 27, 47, 82, 145, 253, 445, 781, 1369, 2405, 4219, 7405, 12998, 22809, 40035, 70263, 123316, 216434, 379854, 666680, 1170079, 2053582, 3604217, 6325695, 11102130, 19485175, 34198108, 60020567, 105341129, 184882533, 324484395

Offset: 0

Ilya Gutkovskiy, Oct 17 2017

nonn

			G.f. =  1 + x + 2*x^2 + 3*x^3 + 5*x^4 + 9*x^5 + 15*x^6 + 27*x^7 + 47*x^8 + 82*x^9 + 145*x^10 + ... = 1/(1 - x - x^2/(1 - x^3 - x^5/(1 - x^9 - x^15/(1 - x^27 - x^47/(1 - x^82 - x^145/(1 - ...)))))).

Cf. A088352, A213411.

A307543 G.f. A(x) satisfies: A(x) = 1/(1 + (-x)^a(0)/(1 + (-x)^a(1)/(1 + (-x)^a(2)/(1 + (-x)^a(3)/(1 + ...))))), a continued fraction.

Original entry on oeis.org

1, 1, 2, 4, 7, 12, 21, 37, 66, 118, 210, 373, 662, 1175, 2087, 3709, 6592, 11714, 20813, 36977, 65695, 116722, 207389, 368486, 654716, 1163271, 2066840, 3672256, 6524693, 11592791, 20597577, 36596883, 65023721, 115531233, 205270716, 364715855, 648010941, 1151357116

Offset: 0

Ilya Gutkovskiy, Apr 14 2019

nonn

			G.f.: A(x) = 1 + x + 2*x^2 + 4*x^3 + 7*x^4 + 12*x^5 + 21*x^6 + 37*x^7 + 66*x^8 + ... = 1/(1 - x/(1 - x/(1 + x^2/(1 + x^4/(1 - x^7/(1 + ...)))))).

Cf. A213411.

cp's OEIS Frontend

A291419 G.f. A(x) = Sum_{n>=0} a(n)x^n satisfies A(x) = 1/(1 - a(0)x^a(0)/(1 - a(1)x^a(1)/(1 - a(2)x^a(2)/(1 - ...)))), a continued fraction.

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A293855 G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies A(x) = 1/(1 - x^a(1) - x^a(2)/(1 - x^a(3) - x^a(4)/(1 - x^a(5) - x^a(6)/(1 - ... )))), a continued fraction.

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A307543 G.f. A(x) satisfies: A(x) = 1/(1 + (-x)^a(0)/(1 + (-x)^a(1)/(1 + (-x)^a(2)/(1 + (-x)^a(3)/(1 + ...))))), a continued fraction.

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cp's OEIS Frontend

A291419 G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies A(x) = 1/(1 - a(0)*x^a(0)/(1 - a(1)*x^a(1)/(1 - a(2)*x^a(2)/(1 - ...)))), a continued fraction.

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A293855 G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies A(x) = 1/(1 - x^a(1) - x^a(2)/(1 - x^a(3) - x^a(4)/(1 - x^a(5) - x^a(6)/(1 - ... )))), a continued fraction.

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A307543 G.f. A(x) satisfies: A(x) = 1/(1 + (-x)^a(0)/(1 + (-x)^a(1)/(1 + (-x)^a(2)/(1 + (-x)^a(3)/(1 + ...))))), a continued fraction.

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A291419 G.f. A(x) = Sum_{n>=0} a(n)x^n satisfies A(x) = 1/(1 - a(0)x^a(0)/(1 - a(1)x^a(1)/(1 - a(2)x^a(2)/(1 - ...)))), a continued fraction.