|
| |
|
|
A126646
|
|
a(n) = 2^(n+1) - 1.
|
|
22
|
|
|
|
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. Ex: 3^2+7=16; 7^2+15=64; 15^2+31=256; etc. - 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
|
Cf. A125630, A125945, A125947, A125948, A125940, A125909, A125908, A125880, A125897, A125904, A125858.
Cf. A000079, A000225, A168604.
Cf. A261461, A261922.
Sequence in context: A213248 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
|
| |
|
|
