A297928 a(n) = 2*4^n + 3*2^n - 1.

4, 13, 43, 151, 559, 2143, 8383, 33151, 131839, 525823, 2100223, 8394751, 33566719, 134242303, 536920063, 2147581951, 8590131199, 34360131583, 137439739903, 549757386751, 2199026401279, 8796099313663, 35184384671743, 140737513521151, 562950003752959, 2251799914348543

Offset: 0

Author

Iain Fox, Jan 08 2018

Keywords

• nonn
• easy

Comments

For n > 0, in binary, this is a 1 followed by n-1 0's followed by 10 followed by n 1's.

Examples

			a(0) = 2*4^0 + 3*2^0 - 1 = 4;   in binary, 100.
a(1) = 2*4^1 + 3*2^1 - 1 = 13;  in binary, 1101.
a(2) = 2*4^2 + 3*2^2 - 1 = 43;  in binary, 101011.
a(3) = 2*4^3 + 3*2^3 - 1 = 151; in binary, 10010111.
a(4) = 2*4^4 + 3*2^4 - 1 = 559; in binary, 1000101111.
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Links

• Index entries for linear recurrences with constant coefficients, signature (7,-14,8)

Crossrefs

A lower bound for A296807.

Cf. A000918, A085601.

Programs

Mathematica

Table[2 4^n+3 2^n-1,{n,0,30}] (* or *) LinearRecurrence[{7,-14,8},{4,13,43},30] (* Harvey P. Dale, Apr 22 2018 *)

PARI

a(n) = 2*4^n + 3*2^n - 1

PARI

first(n) = Vec((4 - 15*x + 8*x^2)/((1 - x)*(1 - 2*x)*(1 - 4*x)) + O(x^n))

Formula

G.f.: (4 - 15*x + 8*x^2)/((1 - x)*(1 - 2*x)*(1 - 4*x)).

E.g.f.: 2*e^(4*x) + 3*e^(2*x) - e^x.

a(n) = 7*a(n-1) - 14*a(n-2) + 8*a(n-3), n > 2.

a(n) = A000918(n) + A085601(n).