A147537 Numbers whose binary representation is the concatenation of 2n-1 digits 1 and n digits 0.

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).

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (10,-16).

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

Adjacent sequences: A147534 A147535 A147536 * A147538 A147539 A147540

Keyword

base,easy,nonn

Author

Omar E. Pol, Nov 06 2008

Status

approved