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A251582
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G.f. satisfies: A(x) = A(2*x^2 + x^3)/(1-x).
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3
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1, 1, 3, 4, 16, 28, 63, 111, 391, 907, 2187, 4555, 10843, 24059, 53667, 113503, 291971, 755271, 1951470, 4751194, 11609612, 27858363, 66082059, 152816667, 355501570, 832148914, 1961821400, 4601053219, 10765373983, 25089663963, 58267298334, 134371615378, 311517418324, 733798887871
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OFFSET
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0,3
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COMMENTS
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Conjecture: limit of a(n+1)/a(n) = sqrt(2) + 1.
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LINKS
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EXAMPLE
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G.f.: A(x) = 1 + x + 3*x^2 + 4*x^3 + 16*x^4 + 28*x^5 + 63*x^6 + 111*x^7 +...
such that A(x) = A(2*x^2 + x^3)/(1-x), where:
A(2*x^2+x^3) = 1 + 2*x^2 + x^3 + 12*x^4 + 12*x^5 + 35*x^6 + 48*x^7 + 280*x^8 + 516*x^9 + 1280*x^10 + 2368*x^11 + 6288*x^12 + 13216*x^13 + 29608*x^14 + 59836*x^15 + 178468*x^16 + 463300*x^17 + 1196199*x^18 +...
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MATHEMATICA
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m = 34; A[_] = 1; Do[A[x_] = A[2x^2 + x^3]/(1-x) + O[x]^m // Normal, {m}]; CoefficientList[A[x], x] (* Jean-François Alcover, Nov 03 2019 *)
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PROG
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(PARI) {a(n)=local(A=1+x); for(i=1, #binary(n)+1, A=subst(A, x, 2*x^2+x^3)/(1-x +x*O(x^n))); polcoeff(A, n)}
for(n=0, 50, print1(a(n), ", "))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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