A063481 a(n) = 4^n + 8^n.

2, 12, 80, 576, 4352, 33792, 266240, 2113536, 16842752, 134479872, 1074790400, 8594128896, 68736253952, 549822922752, 4398314946560, 35185445830656, 281479271677952, 2251816993554432, 18014467228958720, 144115462953762816

Offset

0,1

Comments

Shift 2^n+1 left 2n bits.

Links

Harry J. Smith, Table of n, a(n) for n=0,...,200

D. Suprijanto and Rusliansyah, Observation on Sums of Powers of Integers Divisible by Four, Applied Mathematical Sciences, Vol. 8, 2014, no. 45, 2219 - 2226.

Index entries for linear recurrences with constant coefficients, signature (12,-32).

Formula

G.f.: 1/(1-4*x)+1/(1-8*x). E.g.f.: e^(4*x)+e^(8*x). - Mohammad K. Azarian, Jan 11 2009

a(n)=12*a(n-1)-32*a(n-2) with a(0)=2, a(1)=12. - Vincenzo Librandi, Jul 21 2010

G.f.: G(0), where G(k)= 1 + 2^k/(1 - 4*x/(4*x + 2^k/G(k+1) )); (continued fraction). - Sergei N. Gladkovskii, Jul 22 2013

Example

n=3: 23+1 shifted 2*3 bits to the left is 576 because 23+1 in binary is [1, 0, 0, 1] and 576 is [1, 0, 0, 1, 0, 0, 0, 0, 0, 0].

Mathematica

Table[4^n + 8^n, {n, 0, 25}]

Prog

(PARI) for(n=0, 22, print(shift(2^n+1, 2*n)))
(PARI) { for (n=0, 200, write("b063481.txt", n, " ", shift(1, 2*n) + shift(1, 3*n)) ) } \\ Harry J. Smith, Aug 23 2009

Crossrefs

Cf. A000051, A034472, A052539, A034474, A062394, A034491, A062395, A062396, A007689, A063376, A074600 - A074624.

Sequence in context: A270919 A082142 A069723 * A274782 A185020 A052822

Adjacent sequences: A063478 A063479 A063480 * A063482 A063483 A063484

Keyword

easy,nonn

Author

Jason Earls, Jul 28 2001

Extensions

Edited by Robert G. Wilson v, Aug 25 2002

Status

approved