A172011 a(n) = 12*A002605(n).

0, 12, 24, 72, 192, 528, 1440, 3936, 10752, 29376, 80256, 219264, 599040, 1636608, 4471296, 12215808, 33374208, 91180032, 249108480, 680577024, 1859371008, 5079896064, 13878534144, 37916860416, 103590789120, 283015299072, 773212176384, 2112454950912

Offset: 0

Author

Claudio Peruzzi (claudio.peruzzi(AT)gmail.com), Jan 22 2010

Keywords

• nonn
• easy

Comments

The case k=2 in a family of sequences a(n)=G(k,n), G(k,0)=0, G(k,1)=k*(k+4), G(k,n)=k*G(k,n-1)+k*G(k,n-2).

The Binet formula is G(k,n) = (c^n-b^n)*d where d=sqrt(k*(k+4)); c=(k+d)/2; b=(k-d)/2.

The generating functions are k*(k+4)*x/(1-k*x-k*x^2).

The case k=1 is A022088.

Links

• Index entries for linear recurrences with constant coefficients, signature (2,2).

Crossrefs

Cf. A002605, A022088.

Programs

Mathematica

LinearRecurrence[{2,2},{0,12},30] (* Harvey P. Dale, Mar 06 2023 *)

Formula

Binet formula: a(n) = 2*2^n*((-1+3^(1/2))^(-n)-(-1)^n*(1+3^(1/2))^(-n))*3^(1/2) .

G.f.: 12*x/(1-2*x-2*x^2). a(n) = 2*a(n-1)+2*a(n-2).

Extensions

Edited and extended by R. J. Mathar, Jan 23 2010