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A098657 Expansion of (1-x-4x^2)/((1-2x)(1-8x^2)). 2
1, 1, 6, 4, 40, 16, 288, 64, 2176, 256, 16896, 1024, 133120, 4096, 1056768, 16384, 8421376, 65536, 67239936, 262144, 537395200, 1048576, 4297064448, 4194304, 34368126976, 16777216, 274911461376, 67108864, 2199157473280, 268435456 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Let A=[1,2,1;2,0,-2;1,-2,1] the 3 X 3 symmetric Krawtchouk matrix. Than a(n) is the 1,1 element of A^n.

REFERENCES

P. Feinsilver, J. Kocik, Krawtchouk matrices from classical and quantum walks, Contemporary Mathematics, 287 2001, pp. 83-96.

LINKS

Table of n, a(n) for n=0..29.

Index entries for linear recurrences with constant coefficients, signature (2,8,-16).

FORMULA

a(n)=2^((3n-4)/2)(1+(-1)^n)+2^(n-1); a(n)=2a(n-1)+8a(n-2)-16a(n-3).

CROSSREFS

Cf. A098655, A098656.

Sequence in context: A038258 A298776 A114330 * A126936 A333813 A327370

Adjacent sequences:  A098654 A098655 A098656 * A098658 A098659 A098660

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Sep 19 2004

STATUS

approved

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Last modified June 20 12:49 EDT 2021. Contains 345164 sequences. (Running on oeis4.)