A321483 a(n) = 7*2^n + (-1)^n.

8, 13, 29, 55, 113, 223, 449, 895, 1793, 3583, 7169, 14335, 28673, 57343, 114689, 229375, 458753, 917503, 1835009, 3670015, 7340033, 14680063, 29360129, 58720255, 117440513, 234881023, 469762049, 939524095, 1879048193, 3758096383, 7516192769, 15032385535

Offset: 0

Author

Paul Curtz, Nov 11 2018

Keywords

• nonn
• easy

Comments

Difference table:

8, 13, 29, 55, 113, 223, 449, ...

5, 16, 26, 58, 110, 226, 446, 898, ...

11, 10, 32, 52, 116, 220, 452, 892, 1796, ...

-1, 22, 20, 64, 104, 232, 440, 904, 1784, 3592, ...

-2, 44, 40, 128, 208, 464, 880, 1808, 3568, 7184, ...

etc.

Every diagonal is a sequence of the form k*2^m.

a(n) is divisible by

. 5 if n is a term of A004767,

. 11 if n is a term of A016885,

. 13 if n is a term of A017533.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,2).

Crossrefs

Cf. A000079, A001045, A005029, A010710, A014551, A062092, A062510, A070366, A175805, A199207, A206372.

Cf. A033999, A005009.

Subsequence of A001651, A160543, A160544.

Programs

Mathematica

a[n_] := 7*2^n + (-1)^n ; Array[a, 32, 0] (* Amiram Eldar, Nov 12 2018 *)
CoefficientList[Series[E^-x + 7 E^(2 x), {x, 0, 20}], x]*Table[n!, {n, 0, 20}] (* Stefano Spezia, Nov 12 2018 *)
LinearRecurrence[{1,2},{8,13},40] (* Harvey P. Dale, Mar 18 2022 *)

PARI

Vec((8 + 5*x) / ((1 + x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, Nov 11 2018

Formula

O.g.f.: (8 + 5*x) / ((1 + x)*(1 - 2*x)). - Colin Barker, Nov 11 2018

E.g.f.: exp(-x) + 7*exp(2*x). - Stefano Spezia, Nov 12 2018

a(n) = a(n-1) + 2*a(n-2).

a(n) = 2*a(n-1) + 3*(-1)^n for n>0, a(0)=8.

a(2*k) = 7*4^k + 1, a(2*k+1) = 14*4^k - 1.

a(n) = A014551(n) + A014551(n-1) + A014551(n-2).

a(n) = 2^(n+3) - 3*A001045(n).

a(n) mod 9 = A070366(n+3).

a(n) + a(n+1) = 21*2^n.

Extensions

Two terms corrected, and more terms added by Colin Barker, Nov 11 2018