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A098646 Trace sequence of 3 X 3 Krawtchouk matrix. 4
3, 2, 12, 8, 48, 32, 192, 128, 768, 512, 3072, 2048, 12288, 8192, 49152, 32768, 196608, 131072, 786432, 524288, 3145728, 2097152, 12582912, 8388608, 50331648, 33554432, 201326592, 134217728, 805306368, 536870912, 3221225472, 2147483648 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Let A=[1,1,1;2,0,-2;1,-1,1], the 3 X 3 Krawtchouk matrix. Then a(n)=trace(A^n).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,4)

FORMULA

G.f.: (3+2*x)/((1+2*x)*(1-2*x)).

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

Recurrence: a(n) = 4a(n-2), a(0)=3, a(1)=2. - Ralf Stephan, Jul 17 2013

a(2n+1)=A081294(n+1). a(2n)=A002001(n+1). - R. J. Mathar, Nov 11 2013

PROG

(MAGMA) [(-2)^n+2*2^n: n in [0..45]]; // Vincenzo Librandi, Jun 11 2011

CROSSREFS

Cf. A074535, A098647.

Sequence in context: A122407 A232752 A195200 * A129925 A258206 A267011

Adjacent sequences:  A098643 A098644 A098645 * A098647 A098648 A098649

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Sep 18 2004

STATUS

approved

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Last modified April 8 14:52 EDT 2020. Contains 333314 sequences. (Running on oeis4.)