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

Author

Paul Barry, Sep 18 2004

Keywords

• easy
• nonn

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)

Crossrefs

Cf. A074535, A098647.

Programs

Magma

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

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