OFFSET
0,5
COMMENTS
a(n) = 0 iff n == {0, 1, 2 or 3} (mod 8). - Robert G. Wilson v, Nov 12 2004
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
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[4*x^4*(2+x)/(1-2*x+2*x^2-4*x^4+8*x^5-8*x^6), {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^4*(2+x)/(1-2*x+2*x^2-4*x^4+8*x^5-8*x^6)+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012
(Magma) R<x>:=PowerSeriesRing(Integers(), 60); [0, 0, 0, 0] cat Coefficients(R!( 4*x^4*(2+x)/(1-2*x+2*x^2-4*x^4+8*x^5-8*x^6) )); // G. C. Greubel, Apr 01 2024
(SageMath)
def A100212_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 4*x^4*(2+x)/(1-2*x+2*x^2-4*x^4+8*x^5-8*x^6) ).list()
A100212_list(60) # G. C. Greubel, Apr 01 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Creighton Dement, Nov 08 2004
EXTENSIONS
More terms from Robert G. Wilson v, Nov 12 2004
STATUS
approved