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Maximal term in row n of sequence A240388 when regarded as a triangle.
1

%I #33 Oct 19 2021 12:37:54

%S 1,1,2,4,6,9,17,25,40,72,106,169,305,449,716,1292,1902,3033,5473,8057,

%T 12848,23184,34130,54425,98209,144577,230548,416020,612438,976617,

%U 1762289,2594329,4137016,7465176,10989754,17524681,31622993,46553345

%N Maximal term in row n of sequence A240388 when regarded as a triangle.

%H J. 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_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,4,0,0,1).

%F G.f.: (x^2+x^3+2*x^4+2*x^6+x^7+2*x^10)/(1-4*x^3-x^6).

%F a(3*n-1) = A001076(n). a(3*n) = A048875(n-1). - _R. J. Mathar_, Jul 05 2014

%F a(n) = 4*a(n-3) + a(n-6). - _Harvey P. Dale_, Apr 08 2015

%F a(3*n+1) = 2*Lucas(3*n-3) + Fibonacci(3*n-3)/2 for n>1. - _Greg Dresden_, Oct 17 2021

%p A244470 := proc(n)

%p coeftayl( (x^2+x^3+2*x^4+2*x^6+x^7+2*x^10)/(1-4*x^3-x^6),x=0,n) ;

%p end proc:

%p seq(A244470(n), n=1..50) ; # _R. J. Mathar_, Jul 05 2014

%t CoefficientList[Series[(1 + x + 2*x^2 + 2*x^4 + x^5 + 2*x^8)/(1 - 4*x^3 - x^6), {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Jul 05 2014 *)

%t LinearRecurrence[{0,0,4,0,0,1},{1,1,2,4,6,9,17,25,40},40] (* _Harvey P. Dale_, Apr 08 2015 *)

%Y Cf. A002487, A240388.

%Y Trisections: A001076, A048875.

%K nonn,easy

%O 2,3

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