A020714 a(n) = 5 * 2^n.

5, 10, 20, 40, 80, 160, 320, 640, 1280, 2560, 5120, 10240, 20480, 40960, 81920, 163840, 327680, 655360, 1310720, 2621440, 5242880, 10485760, 20971520, 41943040, 83886080, 167772160, 335544320, 671088640, 1342177280, 2684354560, 5368709120, 10737418240

Offset

0,1

Comments

Same as Pisot sequences E(5,10), L(5,10), P(5,10), T(5,10). See A008776 for definitions of Pisot sequences.

The first differences are the sequence itself. - Alexandre Wajnberg & Eric Angelini, Sep 07 2005

5 times powers of 2. - Omar E. Pol, Dec 16 2008

Subsequence of A051916. - Reinhard Zumkeller, Mar 20 2010

With the addition of "2, 3," at the beginning, this sequence gives terms (n + 3) through the first term greater than 2^n, for n odd, of the negabinary Keith sequence for 2^n, thus proving that with the exception of 2 itself, no odd-indexed power of 2 is a negabinary Keith number (see A188381). - Alonso del Arte, Feb 02 2012

Let b(0) = 5 and b(n+1) = the smallest number not in the sequence such that b(n+1) - Product_{i=0..n} b(i) divides b(n+1) - Sum_{i=0..n} b(i). Then b(n+2) = a(n) for n > 0. - Derek Orr, Jan 15 2015

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..238

John Elias, Illustration: Alternating Tetrahedrons of Tetrahedrons

Tanya Khovanova, Recursive Sequences.

Petro Kosobutskyy, Anastasiia Yedyharova, and Taras Slobodzyan, From Newton's binomial and Pascal's triangle to Collatz's problem, Comp. Des. Sys., Theor. Practice (2023) Vol. 5, No. 1, 121-127.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1003.

Everett Sullivan, Linear chord diagrams with long chords, arXiv preprint arXiv:1611.02771 [math.CO], 2016. See Table 1.

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

Formula

a(n) = 5*2^n. a(n) = 2*a(n-1).

G.f.: 5/(1-2*x).

If m is a term greater than 5 of this sequence then m = 5*phi(phi(m)). - Farideh Firoozbakht, Aug 16 2005

a(n) = A118416(n+1,3) for n>2. - Reinhard Zumkeller, Apr 27 2006

a(n) = A000079(n)*5. - Omar E. Pol, Dec 16 2008

a(n) = A173786(n+2,n) for n > 1. - Reinhard Zumkeller, Feb 28 2010

a(n) = A001045(n+4) - A001045(n). - Paul Curtz, Nov 08 2012

Sum_{n>=1} 1/a(n) = 2/5. - Amiram Eldar, Oct 28 2020

E.g.f.: 5*exp(2*x). - Stefano Spezia, May 15 2021

Mathematica

Table[5*2^n, {n, 0, 31}] (* Vladimir Joseph Stephan Orlovsky, Dec 16 2008 *)
NestList[2#&, 5, 40] (* Harvey P. Dale, Mar 13 2022 *)

Prog

(Magma) [5*2^n: n in [0..40]]; // Vincenzo Librandi, Apr 28 2011
(PARI) a(n)=5<<n \\ Charles R Greathouse IV, Sep 24 2015

Crossrefs

Row sums of (4, 1)-Pascal triangle A093561.

Row sums of (9, 1)-Pascal triangle A093644.

Row sums of (1, 4)-Pascal triangle A095666 (with leading 4).

Cf. A000079, A001045, A008776, A051916, A118416, A173786, A188381.

Sequence in context: A210677 A193839 A323831 * A146523 A102260 A023383

Adjacent sequences: A020711 A020712 A020713 * A020715 A020716 A020717

Keyword

nonn,easy

Author

David W. Wilson

Status

approved