A215203 - OEIS

A215203

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.

0, 1, 11, 183, 5871, 375775, 48099263, 12313411455, 6304466665215, 6455773865180671, 13221424875890015231, 54154956291645502388223, 443637401941159955564326911, 7268555193403964711965932118015, 238176016577461115681699663643131903

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OFFSET

0,3

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..80

FORMULA

a(0)=0, a(n) = a(n-1)*2^(n+1) + 2^n - 1.

a(n)*2 + A076131(n+1) + 1 = 2^A000217(n+1).

EXAMPLE

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.

MATHEMATICA

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 *)

PROG

(Python)

a = 0

for n in range(1, 10):

print(a, end=', ')

a = a*(2**(n+1)) + 2**n - 1

CROSSREFS

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.

Sequence in context: A068648 A209351 A287062 * A034787 A001408 A298643

Adjacent sequences: A215200 A215201 A215202 * A215204 A215205 A215206

KEYWORD

nonn,base,easy,changed

AUTHOR

Alex Ratushnyak, Aug 05 2012

STATUS

approved