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
Conjecture: G.f.: ( 3-x-5*x^2 ) / ( 1-3*x-x^2+4*x^3 ). - R. J. Mathar, Dec 02 2016
MAPLE
A278614T := 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(3, an), op(2, an), op(1, an)+ op(3, an)] ;
else
# apply F1
[op(2, an), op(1, an), op(1, an)+op(3, an)] ;
end if;
end if;
end proc;
A278614 := proc(n)
local a, l;
a := 0 ;
for l from 2^n to 2^(n+1)-1 do
L := A278614T(l) ;
a := a+ L[1]+L[2]+L[3] ;
end do:
a ;
end proc: # R. J. Mathar, Dec 02 2016
MATHEMATICA
A278614T[n_] := A278614T[n] = Module[{an}, If[n == 1, {1, 1, 1}, an = A271487T[Floor[n/2]]; If[EvenQ[n], {an[[3]], an[[2]], an[[1]] + an[[3]]}, {an[[2]], an[[1]], an[[1]] + an[[3]]}]]];
a[n_] := a[n] = Module[{a = 0, l, L}, For[l = 2^n, l <= 2^(n + 1) - 1, l++, L = A278614T[l]; a = a + L[[1]] + L[[2]] + L[[3]]]; a];
Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 0, 19}] (* Jean-François Alcover, Nov 20 2017, after R. J. Mathar *)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Ilya Amburg, Nov 23 2016
EXTENSIONS
More terms from R. J. Mathar, Dec 02 2016
STATUS
approved