login
A278615
Sum of terms in level n of TRIP - Stern sequence associated with permutation triple (e,13,23).
5
3, 8, 21, 56, 148, 394, 1044, 2776, 7364, 19568, 51936, 137960, 366256, 972736, 2582736, 6858880, 18212288, 48363680, 128423232, 341027456, 905565760, 2404701952, 6385502208, 16956417664, 45026632448, 119565922304, 317499868416, 843103631360, 2238811202560, 5945037720064, 15786698462208, 41920680589312, 111317928707072
OFFSET
0,1
LINKS
I. Amburg, K. Dasaratha, L. Flapan, T. Garrity, C. Lee, C. Mihailak, N. Neumann-Chun, S. Peluse, M. Stoffregen, Stern Sequences for a Family of Multidimensional Continued Fractions: TRIP-Stern Sequences, arXiv:1509.05239 [math.CO], 17 Sep 2015.
FORMULA
G.f.: ( 3+2*x-7*x^2 ) / ( 1-2*x-4*x^2+6*x^3 ). - R. J. Mathar, Dec 02 2016
a(n) = A271893(n)+A271894(n)+A271895(n). - R. J. Mathar, Dec 02 2016
MAPLE
A278615T := proc(n)
option remember;
local an, nrecur ;
if n = 1 then
[1, 1, 1] ;
else
an := procname(floor(n/2)) ;
if type(n, 'even') then
# apply F0
[op(1, an)+ op(3, an), op(3, an), op(2, an)] ;
else
# apply F1
[op(1, an), op(1, an)+ op(3, an), op(2, an)] ;
end if;
end if;
end proc;
A278615 := proc(n)
local a, l;
a := 0 ;
for l from 2^n to 2^(n+1)-1 do
L := A278615T(l) ;
a := a+ L[1]+L[2]+L[3] ;
end do:
a ;
end proc: # R. J. Mathar, Dec 02 2016
MATHEMATICA
LinearRecurrence[{2, 4, -6}, {3, 8, 21}, 20] (* Jean-François Alcover, Nov 22 2017, after R. J. Mathar's g.f. *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Amburg, Nov 23 2016
EXTENSIONS
More terms from R. J. Mathar, Dec 02 2016
STATUS
approved