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A215203
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a(0) = 0, a(n) = a(n - 1)*2^(n + 1) + 2^n - 1. That is, add one 0 and n 1's to the binary representation of previous term.
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3
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0, 1, 11, 183, 5871, 375775, 48099263, 12313411455, 6304466665215, 6455773865180671, 13221424875890015231, 54154956291645502388223, 443637401941159955564326911, 7268555193403964711965932118015, 238176016577461115681699663643131903
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OFFSET
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0,3
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LINKS
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FORMULA
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a(0)=0, a(n) = a(n-1)*2^(n+1) + 2^n - 1.
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EXAMPLE
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Binary representations:
a(0): 0;
a(1): 1;
a(2): 1011;
a(3): 10110111;
a(4): 1011011101111;
a(5): 1011011101111011111;
a(6): 10110111011110111110111111;
a(7): 1011011101111011111011111101111111;
a(8): 1011011101111011111011111101111111011111111, etc.
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MATHEMATICA
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nxt[{n_, a_}]:={n+1, FromDigits[Join[IntegerDigits[a, 2], PadRight[{0}, n+2, 1]], 2]}; NestList[nxt, {0, 0}, 15][[All, 2]] (* Harvey P. Dale, Feb 11 2023 *)
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PROG
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(Python)
a = 0
for n in range(1, 10):
#print 'a('+str(n-1)+')', bin(a)[2:], a
print a,
a = a*(2**(n+1)) + 2**n - 1
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CROSSREFS
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Cf. A076131: add n 0's and one 1 to the binary representation of previous term.
Cf. A215172: add n 0's and n 1's to the binary representation of previous term.
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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