login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A126646 a(n) = 2^(n+1) - 1. 30
1, 3, 7, 15, 31, 63, 127, 255, 511, 1023, 2047, 4095, 8191, 16383, 32767, 65535, 131071, 262143, 524287, 1048575, 2097151, 4194303, 8388607, 16777215, 33554431, 67108863, 134217727, 268435455, 536870911, 1073741823, 2147483647 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is the number of integers k less than 10^n such that the decimal representation of k lacks the digits 1,2,3,4,5,6 and 7 and at least one of the digits 8,9.

Partial sums of the powers of 2 (A000079).

a(n-1)^2 + a(n) is a(2n)+1, a square. Examples: 3^2 + 7 = 16; 7^2 + 15 = 64; 15^2 + 31 = 256. - Vincenzo Librandi and Ralf Stephan, Nov 23 2010

a(n) is the number of elements (all m-dimensional faces) in an n-dimensional simplex (0 <= m <= n). - Sergey Pavlov, Aug 15 2015

A261461(a(n)) != A261922(a(n)). - Reinhard Zumkeller, Sep 17 2015

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Jerry Metzger and Thomas Richards, A Prisoner Problem Variation, Journal of Integer Sequences, Vol. 18 (2015), Article 15.2.7.

Wikipedia, Simplex Elements (see last column of table).

Index entries for linear recurrences with constant coefficients, signature (3,-2).

FORMULA

G.f.: 1/ ( (1-2*x)*(1-x) ). - R. J. Mathar, Dec 02 2013

a(n) = 3*a(n-1) - 2*a(n-2), n > 1. - Wesley Ivan Hurt, Aug 21 2015

EXAMPLE

a(8) = 2^9 - 1 = 511.

MAPLE

A126646:=n->2*2^n-1; seq(A126646(n), n=0..50); # Wesley Ivan Hurt, Dec 02 2013

MATHEMATICA

Table[2^(n + 1) - 1, {n, 0, 50}] (* Wesley Ivan Hurt, Dec 02 2013 *)

LinearRecurrence[{3, -2}, {1, 3}, 40] (* Harvey P. Dale, Mar 23 2018 *)

PROG

(PARI) first(m)=vector(m, i, i--; 2^(i+1)-1) /* Anders Hellström, Aug 19 2015 */

(MAGMA) [2^(n+1)-1: n in [0.. 35]]; // Vincenzo Librandi, Aug 20 2015

(Haskell)

a126646 = (subtract 1) . (2 ^) . (+ 1)

a126646_list = iterate ((+ 1) . (* 2)) 1

-- Reinhard Zumkeller, Sep 17 2015

CROSSREFS

Essentially the same as A000225.

Cf. A125630, A125945, A125947, A125948, A125940, A125909, A125908, A125880, A125897, A125904, A125858.

Cf. A000079, A168604.

Cf. A261461, A261922.

Sequence in context: A336700 A097002 A060152 * A000225 A225883 A255047

Adjacent sequences:  A126643 A126644 A126645 * A126647 A126648 A126649

KEYWORD

nonn,easy

AUTHOR

Aleksandar M. Janjic and Milan Janjic, Feb 08 2007, Feb 13 2007

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 26 20:15 EST 2021. Contains 341643 sequences. (Running on oeis4.)