A098646 Trace sequence of 3 X 3 Krawtchouk matrix.

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

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: A346122 A232752 A195200 * A129925 A267011 A258206

Adjacent sequences: A098643 A098644 A098645 * A098647 A098648 A098649

Keyword

easy,nonn

Author

Paul Barry, Sep 18 2004

Status

approved