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A147537
Numbers whose binary representation is the concatenation of 2n-1 digits 1 and n digits 0.
8
2, 28, 248, 2032, 16352, 131008, 1048448, 8388352, 67108352, 536869888, 4294965248, 34359734272, 274877898752, 2199023239168, 17592186011648, 140737488289792, 1125899906711552, 9007199254478848, 72057594037403648, 576460752302374912, 4611686018425290752
OFFSET
1,1
COMMENTS
a(n) is the number whose binary representation is A138118(n).
FORMULA
From Colin Barker, Nov 04 2012: (Start)
a(n) = 2^(n-1)*(4^n - 2) = 2*A147590(n).
a(n) = 10*a(n-1) - 16*a(n-2).
G.f.: 2*x*(1+4*x)/((1-2*x)*(1-8*x)). (End)
MAPLE
seq(2^n*(2^(2*n-1)-1), n = 1..20); # G. C. Greubel, Jan 12 2020
MATHEMATICA
Table[FromDigits[Join[Table[1, {2n - 1}], Table[0, {n}]], 2], {n, 1, 20}] (* Stefan Steinerberger, Nov 11 2008 *)
PROG
(PARI) vector(20, n, 2^n*(2^(2*n-1)-1)) \\ G. C. Greubel, Jan 12 2020
(Magma) [2^n*(2^(2*n-1)-1): n in [1..20]] // G. C. Greubel, Jan 12 2020
(Sage) [2^n*(2^(2*n-1)-1) for n in (1..20)] # G. C. Greubel, Jan 12 2020
(GAP) List([1..20], n-> 2^n*(2^(2*n-1)-1)); # G. C. Greubel, Jan 12 2020
(Python)
def a(n): return ((1 << (2*n-1)) - 1) << n
print([a(n) for n in range(1, 22)]) # Michael S. Branicky, Feb 28 2021
CROSSREFS
Cf. A138118.
Sequence in context: A001759 A243475 A019441 * A183067 A056261 A326248
KEYWORD
base,easy,nonn
AUTHOR
Omar E. Pol, Nov 06 2008
STATUS
approved