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

0,1

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).

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.

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 *)

Prog

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

Crossrefs

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

Cf. A033999, A005009.

Subsequence of A001651, A160543, A160544.

Sequence in context: A057097 A246639 A287922 * A096371 A354595 A063585

Adjacent sequences: A321480 A321481 A321482 * A321484 A321485 A321486

Keyword

nonn,easy

Author

Paul Curtz, Nov 11 2018

Extensions

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

Status

approved