A244473 3rd-largest term in n-th row of Stern's diatomic triangle A002487.

1, 3, 5, 11, 18, 30, 49, 80, 129, 209, 338, 547, 885, 1432, 2317, 3749, 6066, 9815, 15881, 25696, 41577, 67273, 108850, 176123, 284973, 461096, 746069, 1207165, 1953234, 3160399, 5113633, 8274032, 13387665, 21661697, 35049362, 56711059, 91760421

Offset: 2

Author

N. J. A. Sloane, Jul 01 2014

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 2..1000
• Jennifer Lansing, Largest Values for the Stern Sequence, J. Integer Seqs., 17 (2014), #14.7.5.
• Index entries for linear recurrences with constant coefficients, signature (1,1).

Crossrefs

Cf. A002487, A244472-A244476.

Programs

Maple

A244473 := proc(n)
    if n < 8 then
        op(n,[-1,1,3,5,11,18,30]) ;
    else
        combinat[fibonacci](n+1)+5*combinat[fibonacci](n-4) ;
    end if;
end proc:
seq(A244473(n),n=2..50) ; # R. J. Mathar, Jul 05 2014

Mathematica

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

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

Formula

a(n) = a(n-1)+a(n-2) for n>9. - Colin Barker, Jul 10 2015

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