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A100212 Expansion of (x^5 + 2*x^4)/(1/2*x^2 - 2*x^6 + 2*x^5 - x^4 - 1/2*x + 1/4). 1
0, 0, 0, 0, 8, 20, 24, 8, 0, 0, 0, 0, 128, 320, 384, 128, 0, 0, 0, 0, 2048, 5120, 6144, 2048, 0, 0, 0, 0, 32768, 81920, 98304, 32768, 0, 0, 0, 0, 524288, 1310720, 1572864, 524288, 0, 0, 0, 0, 8388608, 20971520, 25165824, 8388608, 0, 0, 0, 0, 134217728, 335544320 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

a(n) = 0 iff n == {0, 1, 2 or 3} (mod 8). - Robert G. Wilson v, Nov 12 2004

LINKS

Table of n, a(n) for n=0..53.

Index entries for linear recurrences with constant coefficients, signature (2, -2, 0, 4, -8, 8).

FORMULA

a(8n+4) = a(8n+7) = 2^(4n+3), a(8n+5) = (5/2)*2^(4n+3), a(8n+6) = 3*2^(4n+3), a(8n+8) = 0, a(8n+9) = 0, a(8n+10) = 0, a(8n+11) = 0.

(a(n)) = negseq(.5 'j + .5 'k + .5 j' + .5 k' + 1 'ii' + 1 e)

a(0)=0, a(1)=0, a(2)=0, a(3)=0, a(4)=8, a(5)=20, a(n) = 2*a(n-1) - 2*a(n-2) + 4*a(n-4) - 8*a(n-5) + 8*a(n-6). - Harvey P. Dale, Oct 10 2012

MATHEMATICA

CoefficientList[ Series[(x^5 + 2*x^4)/(x^2/2 - 2*x^6 + 2*x^5 - x^4 - x/2 + 1/4), {x, 0, 55}], x] (* Robert G. Wilson v, Nov 12 2004 *)

LinearRecurrence[{2, -2, 0, 4, -8, 8}, {0, 0, 0, 0, 8, 20}, 60] (* Harvey P. Dale, Oct 10 2012 *)

PROG

(PARI) Vec((4*x^5+8*x^4)/(-8*x^6+8*x^5-4*x^4+2*x^2-2*x+1)+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012

CROSSREFS

Cf. A100213, A038503, A009116.

Sequence in context: A214457 A205226 A205318 * A083094 A164916 A207190

Adjacent sequences:  A100209 A100210 A100211 * A100213 A100214 A100215

KEYWORD

nonn,easy

AUTHOR

Creighton Dement, Nov 08 2004

EXTENSIONS

More terms from Robert G. Wilson v, Nov 12 2004

STATUS

approved

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Last modified August 20 20:09 EDT 2017. Contains 290837 sequences.