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A244472 2nd-largest term in n-th row of Stern's diatomic triangle A002487.

%I A244472 #19 Sep 08 2022 08:46:08
%S A244472 1,2,4,7,12,19,31,50,81,131,212,343,555,898,1453,2351,3804,6155,9959,
%T A244472 16114,26073,42187,68260,110447,178707,289154,467861,757015,1224876,
%U A244472 1981891,3206767,5188658,8395425,13584083,21979508,35563591,57543099
%N A244472 2nd-largest term in n-th row of Stern's diatomic triangle A002487.
%H A244472 Colin Barker, <a href="/A244472/b244472.txt">Table of n, a(n) for n = 1..1000</a>
%H A244472 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 A244472 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,1).
%F A244472 a(n) = A013655(n-1), n>3.
%F A244472 a(n) = a(n-1)+a(n-2), n>5. - _Colin Barker_, Jul 10 2015
%F A244472 G.f.: -x*(x^4+x^3+x^2+x+1) / (x^2+x-1). - _Colin Barker_, Jul 10 2015
%p A244472 A244472 := proc(n)
%p A244472     if n < 4 then
%p A244472         op(n,[1,2,4]) ;
%p A244472     else
%p A244472         combinat[fibonacci](n+2)-combinat[fibonacci](n-3) ;
%p A244472     end if;
%p A244472 end proc:
%p A244472 seq(A244472(n),n=1..50) ; # _R. J. Mathar_, Jul 05 2014
%t A244472 CoefficientList[Series[-(x^4 + x^3 + x^2 + x + 1)/(x^2 + x - 1), {x, 0, 50}], x] (* _Wesley Ivan Hurt_, Jul 10 2015 *)
%t A244472 Join[{1, 2, 4}, LinearRecurrence[{1, 1}, {7, 12}, 50]] (* _Vincenzo Librandi_, Jul 11 2015 *)
%o A244472 (PARI) Vec(-x*(x^4+x^3+x^2+x+1)/(x^2+x-1) + O(x^100)) \\ _Colin Barker_, Jul 10 2015
%o A244472 (Magma) I:=[1, 2, 4, 7, 12]; [n le 5 select I[n] else Self(n-1)+Self(n-2): n in [1..40]]; // _Wesley Ivan Hurt_, Jul 10 2015
%Y A244472 Cf. A002487, A013655, A100545 (bisection).
%Y A244472 Cf. A244473, A244474, A244475, A244476.
%K A244472 nonn,easy
%O A244472 1,2
%A A244472 _N. J. A. Sloane_, Jul 01 2014