A136751
G.f.: A(x) = ...o x/(1-x^4) o x/(1-x^3) o x/(1-x^2) o x/(1-x), composition of functions x/(1-x^n) for n = 1,2,3,...
Original entry on oeis.org
1, 1, 2, 5, 13, 36, 104, 310, 943, 2913, 9112, 28805, 91893, 295484, 956671, 3115805, 10200445, 33544983, 110755143, 366976365, 1219814018, 4066305982, 13590864072, 45534416250, 152895704998, 514446539489, 1734239511881
Offset: 0
G.f.: A(x) is the limit of composition of functions x/(1-x^n):
F_1(x) = x/(1-x)
F_2(x) = x/(1-x^2) o F_1(x) = x + x^2 + 2x^3 + 4x^4 + 8x^5 + 16x^6 +...
F_3(x) = x/(1-x^3) o F_2(x) = x + x^2 + 2x^3 + 5x^4 + 12x^5 + 30x^6 +...
F_4(x) = x/(1-x^4) o F_3(x) = x + x^2 + 2x^3 + 5x^4 + 13x^5 + 35x^6 +...
F_5(x) = x/(1-x^5) o F_4(x) = x + x^2 + 2x^3 + 5x^4 + 13x^5 + 36x^6 +...
F_6(x) = x/(1-x^6) o x/(1-x^5) o x/(1-x^4) o x/(1-x^3) o x/(1-x^2) o x/(1-x) =
x + x^2 + 2*x^3 + 5*x^4 + 13*x^5 + 36*x^6 + 104*x^7 + 309*x^8 + 934*x^9 + ...
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{a(n)=local(A=x+x*O(x^n));if(n<=0,0,for(i=1,n,A=A/(1-A^i));polcoeff(A,n))}
for(n=1,40,print1(a(n),", "))
A136752
G.f.: A(x) = x/(1-x) o x/(1-x^2) o x/(1-x^4) o x/(1-x^8) o..., composition of functions x/(1 - x^{2^n}) for n=0,1,2,3,...
Original entry on oeis.org
1, 1, 2, 3, 6, 10, 19, 33, 61, 108, 198, 354, 645, 1159, 2106, 3795, 6874, 12405, 22457, 40560, 73374, 132578, 239782, 433362, 783602, 1416401, 2560953, 4629393, 8369741, 15130440, 27354520, 49451349, 89401972, 161622356, 292191262
Offset: 0
G.f.: A(x) is the limit of composition of functions x/(1-x^{2^n}):
F_0(x) = x/(1-x)
F_1(x) = F_1(x/(1-x^2)) = x + x^2 + 2x^3 + 3x^4 + 5x^5 + 8*x^6 + 13x^7 +...
F_2(x) = F_2(x/(1-x^4)) = x + x^2 + 2x^3 + 3x^4 + 6x^5 + 10x^6 + 19x^7 +...
F_3(x) = x/(1-x) o x/(1-x^2) o x/(1-x^4) o x/(1-x^8) =
x + x^2 + 2x^3 + 3x^4 + 6x^5 + 10x^6 + 19x^7 + 33x^8 + 61x^9 + 108x^10 +...
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{a(n)=local(A=x+x*O(x^n));if(n<=0,0,m=#binary(n+1); for(i=1,m,A=A/(1-A^(2^(m-i))));polcoeff(A,n))}
A136753
G.f.: A(x) = ...o x/(1-x^8) o x/(1-x^4) o x/(1-x^2) o x/(1-x), composition of functions x/(1 - x^{2^n}) for n=...,3,2,1,0.
Original entry on oeis.org
1, 1, 2, 4, 9, 21, 52, 134, 355, 955, 2590, 7052, 19246, 52638, 144368, 397468, 1099720, 3060936, 8577496, 24210808, 68843806, 197176726, 568585576, 1649739332, 4812731846, 14105205846, 41498665884, 122469937048
Offset: 1
G.f.: A(x) is the limit of composition of functions x/(1-x^{2^n}):
F_0(x) = x/(1-x)
F_1(x) = x/(1-x^2) o F_0(x) = x + x^2 + 2x^3 + 4x^4 + 8x^5 + 16x^6 +...
F_2(x) = x/(1-x^4) o F_1(x) = x + x^2 + 2x^3 + 4x^4 + 9x^5 + 21x^6 +...
F_3(x) = x/(1-x^8) o F_2(x) = x + x^2 + 2x^3 + 4x^4 + 9x^5 + 21x^6 +...
F_4(x) = x/(1-x^16) o x/(1-x^8) o x/(1-x^4) o x/(1-x^2) o x/(1-x) =
x + x^2 + 2*x^3 + 4*x^4 + 9*x^5 + 21*x^6 + 52*x^7 + 134*x^8 + 355*x^9 +...
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{a(n)=local(A=x+x*O(x^n));if(n<=0,0,for(i=0,#binary(n+1),A=A/(1-A^(2^i)));polcoeff(A,n))}
A206720
G.f.: A(x) = x/(1-x) o x/(1-x^3) o x/(1-x^5) o x/(1-x^7) o..., a composition of functions x/(1-x^(2*n-1)) for n=1,2,3,...
Original entry on oeis.org
1, 1, 1, 2, 3, 5, 8, 13, 23, 38, 63, 105, 178, 300, 501, 849, 1431, 2405, 4044, 6812, 11491, 19361, 32621, 54946, 92646, 156118, 262964, 443200, 746933, 1258840, 2121343, 3575153, 6025323, 10154336, 17112673, 28839762, 48605300, 81913614, 138049346, 232655873
Offset: 1
G.f.: A(x) = x + x^2 + x^3 + 2*x^4 + 3*x^5 + 5*x^6 + 8*x^7 + 13*x^8 +...
where A(x) is the limit of composition of functions x/(1-x^(2*n-1)):
F_1(x) = x/(1-x)
F_2(x) = F_1(x/(1-x^3)) = x + x^2 + x^3 + 2*x^4 + 3*x^5 + 4*x^6 + 6*x^7 +...
F_3(x) = F_2(x/(1-x^5)) = x + x^2 + x^3 + 2*x^4 + 3*x^5 + 5*x^6 + 8*x^7 +...
F_4(x) = x/(1-x) o x/(1-x^3) o x/(1-x^5) o x/(1-x^7); ...
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{a(n)=local(A=x+x*O(x^n)); if(n<=0, 0, for(i=1, n, A=A/(1-A^(2*(n-i)+1))); polcoeff(A, n))}
for(n=1,45,print1(a(n),", "))
Showing 1-4 of 4 results.
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