A133469 - OEIS

%I #32 Jul 24 2017 08:26:52

%S 1,2,9,23,86,247,849,2578,8521,26567,86214,272183,875681,2780962,

%T 8910729,28377463,90752566,289394807,924662769,2950426418,9423065801,

%U 30076050727,96037511334,306569866423,978832445761,3124821510722

%N a(n) = a(n-1) + 7*a(n-2) for n >= 2, a(0)=1, a(1)=2.

%H Robert Israel, <a href="/A133469/b133469.txt">Table of n, a(n) for n = 0..1981</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1, 7).

%F G.f.: (1+x)/(1-x-7*x^2) .

%F a(n) = Sum_{k=0..n+1} A122950(n+1,k)*6^(n+1-k). - _Philippe Deléham_, Jan 08 2008

%F a(n) = ((29 + 3*sqrt(29))/58)*(0.5 + 0.5*sqrt(29))^n + ((29 - 3*sqrt(29))/58)*(0.5 - 0.5*sqrt(29))^n. - _Richard Choulet_, Nov 20 2008

%p f:= gfun:-rectoproc({a(n) = a(n-1) + 7*a(n-2), a(0)=1, a(1)=2}, a(n), remember):

%p map(f, [$0..50]); # _Robert Israel_, Jul 23 2017

%t LinearRecurrence[{1,7},{1,2},30] (* _Harvey P. Dale_, Dec 09 2013 *)

%o (PARI) x='x+O('x^99); Vec((1+x)/(1-x-7*x^2)) \\ _Altug Alkan_, Jul 23 2017

%K easy,nonn

%O 0,2

%A _Philippe Deléham_, Jan 03 2008