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A013776 a(n) = 2^(4*n+1). 7
2, 32, 512, 8192, 131072, 2097152, 33554432, 536870912, 8589934592, 137438953472, 2199023255552, 35184372088832, 562949953421312, 9007199254740992, 144115188075855872, 2305843009213693952 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n) ~ -Pi*E(2*n)/B(2*n), E(n) Euler number, B(n) Bernoulli number. - Peter Luschny, Oct 28 2012

Equivalently, powers of 2 with final digit 2. - Muniru A Asiru, Mar 15 2019

a(5*n) = {2, 2097152, 2199023255552, ...} has initial and final digit equal 2. - Muniru A Asiru, Apr 17 2019

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Tanya Khovanova, Recursive Sequences

Index to divisibility sequences

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

FORMULA

From Philippe Deléham, Nov 23 2008: (Start)

a(n) = 16*a(n-1), n > 0, a(0) = 2.

G.f.: 2/(1 - 16*x). (End)

From Peter Bala, Nov 29 2015: (Start)

a(n) = Sum_{k = 0..n} binomial(2*k,k)*binomial(4*n + 2 - 2*k, 2*n + 1 - k).

Bisection of A264960. (End)

a(n) = A000079(A016813(n)). - Michel Marcus, Nov 30 2015

a(n) = Sum_{k = 0..2*n} binomial(4*n + 2, 2*k + 1) = A004171(2*n). - Peter Bala, Nov 25 2016

E.g.f.: 2*exp(16*x). - G. C. Greubel, Jun 30 2019

EXAMPLE

G.f. = 2 + 32*x + 512*x^2 + 8192*x^3 + 131072*x^4 + 2097152*x^5 + ...

MAPLE

[2^(4*n+1)$n=0..20]; # Muniru A Asiru, Apr 10 2019

MATHEMATICA

2^(4*Range[0, 20]+1) (* G. C. Greubel, Mar 15 2019 *)

NestList[16#&, 2, 20] (* Harvey P. Dale, Jul 28 2019 *)

PROG

(MAGMA) [2^(4*n+1): n in [0..20]]; // Vincenzo Librandi, Jun 27 2011

(PARI) a(n)=2<<(4*n) \\ Charles R Greathouse IV, Apr 07 2012

(GAP) List([0..20], n->2^(4*n+1)); # Muniru A Asiru, Mar 15 2019

(Sage) [2^(4*n+1) for n in (0..20)] # G. C. Greubel, Mar 15 2019

CROSSREFS

Cf. A000079, A016813, A264960, A004171.

Sequence in context: A163952 A246213 A022028 * A174491 A022019 A010045

Adjacent sequences:  A013773 A013774 A013775 * A013777 A013778 A013779

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 20 12:36 EDT 2019. Contains 328257 sequences. (Running on oeis4.)