A244473 - OEIS

%I #18 Jul 10 2015 08:44:00

%S 1,3,5,11,18,30,49,80,129,209,338,547,885,1432,2317,3749,6066,9815,

%T 15881,25696,41577,67273,108850,176123,284973,461096,746069,1207165,

%U 1953234,3160399,5113633,8274032,13387665,21661697,35049362,56711059,91760421

%N 3rd-largest term in n-th row of Stern's diatomic triangle A002487.

%H Colin Barker, <a href="/A244473/b244473.txt">Table of n, a(n) for n = 2..1000</a>

%H Jennifer Lansing, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Lansing/lansing2.html">Largest Values for the Stern Sequence</a>, J. Integer Seqs., 17 (2014), #14.7.5.

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

%F a(n) = a(n-1)+a(n-2) for n>9. - _Colin Barker_, Jul 10 2015

%F G.f.: -x^2*(x^7+x^6+x^5+2*x^4+3*x^3+x^2+2*x+1) / (x^2+x-1). - _Colin Barker_, Jul 10 2015

%p A244473 := proc(n)

%p     if n < 8 then

%p         op(n,[-1,1,3,5,11,18,30]) ;

%p     else

%p         combinat[fibonacci](n+1)+5*combinat[fibonacci](n-4) ;

%p     end if;

%p end proc:

%p seq(A244473(n),n=2..50) ; # _R. J. Mathar_, Jul 05 2014

%t Join[{1,3,5,11,18,30},LinearRecurrence[{1,1},{49,80},40]] (* _Harvey P. Dale_, Jan 13 2015 *)

%o (PARI) Vec(-x^2*(x^7+x^6+x^5+2*x^4+3*x^3+x^2+2*x+1)/(x^2+x-1) + O(x^100)) \\ _Colin Barker_, Jul 10 2015

%Y Cf. A002487, A244472-A244476.

%K nonn,easy

%O 2,2

%A _N. J. A. Sloane_, Jul 01 2014