A133592 - OEIS

%I #23 Jul 01 2023 09:17:25

%S 1,2,8,28,104,376,1376,5008,18272,66592,242816,885184,3227264,

%T 11765632,42894848,156383488,570136064,2078573056,7577962496,

%U 27627363328,100722501632,367209183232,1338753376256,4880761851904,17794043961344

%N a(n) = 2*a(n-1)+6*a(n-2) for n>=3, a(0)=1, a(1)=2, a(2)=8.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,6).

%F G.f.: (1-2*x^2)/(1-2*x-6*x^2).

%F a(n) = Sum_{k=0..n} A122950(n,k)*2^k .

%F a(n) = ((7+2*sqrt(7))/21)*(1+sqrt(7))^n+((7-2*sqrt(7))/21)*(1-sqrt(7))^n for n=>1. [_Richard Choulet_, Nov 19 2008]

%F a(n) = A083099(n+1) - 2*A083099(n-1). - _R. J. Mathar_, Jun 20 2015

%p A133592 := proc(n)

%p         option remember;

%p         if n <=1 then

%p                 n+1;

%p         elif n = 2 then

%p                 8;

%p         else

%p                 2*procname(n-1)+6*procname(n-2) ;

%p         fi ;

%p end proc: # _R. J. Mathar_, Jul 15 2017

%t Join[{1}, LinearRecurrence[{2, 6}, {2, 8}, 24]] (* _Jean-François Alcover_, Jul 01 2023 *)

%Y Cf. A083099, A122950.

%K easy,nonn

%O 0,2

%A _Philippe Deléham_, Dec 31 2007

%E a(16) corrected by _R. J. Mathar_, Jun 20 2015