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A280173 a(0) = 1, a(n+1) = 2*a(n) + periodic sequence of length 2: repeat [5, -4]. 2
1, 7, 10, 25, 46, 97, 190, 385, 766, 1537, 3070, 6145, 12286, 24577, 49150, 98305, 196606, 393217, 786430, 1572865, 3145726, 6291457, 12582910, 25165825, 50331646, 100663297, 201326590, 402653185, 805306366, 1610612737, 3221225470, 6442450945, 12884901886 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) mod 9 = period 2: repeat [1, 7].

The last digit from 7 is of period 4: repeat [7, 0, 5, 6].

The bisection A096045 = 1, 10, 46, ... is based on Bernoulli numbers.

a(n) is a companion to A051049(n).

With an initial 0, A051049(n) is an autosequence of the first kind.

With an initial 2, this sequence is an autosequence of the second kind.

See the reference.

Difference table:

1,   7, 10, 25, 46,  97, ... = this sequence.

6,   3, 15, 21, 51,  93, ... = 3*A014551(n)

-3, 12,  6, 30, 42, 102, ... = -3 followed by 6*A014551(n).

The main diagonal of the difference table gives A003945: 1, 3, 6, 12, 24, ...

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Wikipedia, Autosuite de nombres, (in French).

Index entries for linear recurrences with constant coefficients, signature (2,1,-2).

FORMULA

a(2n) = 3*4^n - 2, a(2n+1) = 6*4^n + 1.

a(n+2) = a(n) + 9*2^n, a(0) = 1, a(1) = 7.

a(n) = 2*A051049(n+1) - A051049(n).

From Colin Barker, Dec 28 2016: (Start)

a(n) = 3*2^n - 2 for n even.

a(n) = 3*2^n + 1 for n odd.

a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) for n>2.

G.f.: (1 + 5*x - 5*x^2) / ((1 - x)*(1 + x)*(1 - 2*x)).

(End)

a(n) = -1/2 -3/2*(-1)^n + 3*2^n. - Paolo P. Lava, May 18 2017

EXAMPLE

a(0) = 1, a(1) = 2*1 + 5 = 7, a(2) = 2*7 - 4 = 10, a(3) = 2*10 + 5 = 25.

MAPLE

seq(3*2^n-(-1)^n*(1+irem(n+1, 2)), n=0..32); # Peter Luschny, Dec 29 2016

PROG

(PARI) Vec((1 + 5*x - 5*x^2) / ((1 - x)*(1 + x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, Dec 28 2016

CROSSREFS

Cf. A003945, A005010, A010688, A010710, A014551, A051049, A096045, A199116.

Sequence in context: A134329 A175492 A241052 * A229310 A064948 A064950

Adjacent sequences:  A280170 A280171 A280172 * A280174 A280175 A280176

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Dec 28 2016

STATUS

approved

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Last modified August 11 05:13 EDT 2022. Contains 356046 sequences. (Running on oeis4.)