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A274817 a(n) = 2*a(n-1) - a(n-3) + 2*a(n-4) for n>3, a(0)=1, a(1)=-1, a(2)=4, a(3)=8. 3
1, -1, 4, 8, 19, 32, 64, 125, 256, 512, 1027, 2048, 4096, 8189, 16384, 32768, 65539, 131072, 262144, 524285, 1048576, 2097152, 4194307, 8388608, 16777216, 33554429, 67108864, 134217728, 268435459, 536870912, 1073741824, 2147483645, 4294967296, 8589934592 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) mod 9 = 1, 8, 4, 8, 1, 5, 1, 8, 4, 8, 1, 5, ... (repeat).

Difference table for a(n):

1,   -1,   4,  8,  19, 32, ...

-2,   5,   4, 11,  13, 32, ...

7,   -1,   7,  2,  19, 29, ...

-8,   8,  -5, 17,  10, 41, ...

16, -13,  22, -7,  31, 14, ...

-29, 35, -29, 38, -17, 65, ...

... .

The recurrence of the name is valid for every line and the main diagonal which is in A014551.

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (2,0,-1,2).

FORMULA

G.f.: (x^3+6*x^2-3*x+1) / (-2*x^4+x^3-2*x+1). - Colin Barker, Jul 07 2016

a(n) = 2*a(n-1) - a(n-3) + 2*a(n-4) for n>3. - Wesley Ivan Hurt, Jul 07 2016

a(n) = 2^n - sin(n*Pi/3)*(sqrt(3) + 2*sin(2*n*Pi/3)). - Wesley Ivan Hurt, Jul 07 2016

a(n)   = 2^n - period 6: repeat [0, 3, 0, 0, -3, 0].

a(n+1) = 2*a(n) + period 6: repeat [-3, 6, 0, 3, -6, 0].

a(n+3) = -a(n) + 9*2^n.

a(n)   = A014551(n) - A057079(n).

MAPLE

A274817:=n->2^n - sin(n*Pi/3)*(sqrt(3) + 2*sin(2*n*Pi/3)): seq(A274817(n), n=0..40); # Wesley Ivan Hurt, Jul 07 2016

MATHEMATICA

Table[2^n - Sin[n*Pi/3] (Sqrt[3] + 2 Sin[2*n*Pi/3]), {n, 0, 40}] (* Wesley Ivan Hurt, Jul 07 2016 *)

LinearRecurrence[{2, 0, -1, 2}, {1, -1, 4, 8}, 100] (* G. C. Greubel, Jul 07 2016 *)

PROG

(PARI) Vec((x^3+6*x^2-3*x+1)/(-2*x^4+x^3-2*x+1) + O(x^40)) \\ Colin Barker, Jul 07 2016

CROSSREFS

Cf. A000079, A014551, A057079.

Sequence in context: A272542 A280114 A162362 * A130887 A049933 A301746

Adjacent sequences:  A274814 A274815 A274816 * A274818 A274819 A274820

KEYWORD

sign,easy

AUTHOR

Paul Curtz, Jul 07 2016

EXTENSIONS

One term corrected and more terms added by Colin Barker, Jul 07 2016

STATUS

approved

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Last modified January 19 09:35 EST 2020. Contains 331048 sequences. (Running on oeis4.)