|
| |
|
|
A278616
|
|
Sum of terms in level n of TRIP - Stern sequence associated with permutation triple (e,13,132).
|
|
5
|
|
|
|
3, 8, 21, 56, 148, 393, 1041, 2761, 7318, 19403, 51436, 136366, 361513, 958413, 2540831, 6735996, 17857733, 47342548, 125509476, 332737401
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,1
|
|
|
LINKS
|
Table of n, a(n) for n=0..19.
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.: ( -3-5*x-x^2 ) / ( -1+x+4*x^2+x^3 ). - R. J. Mathar, Dec 02 2016
|
|
|
MAPLE
|
A278616T := 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(2, an), op(1, an)+ op(3, an), op(1, an)] ;
end if;
end if;
end proc;
A278616 := proc(n)
local a, l;
a := 0 ;
for l from 2^n to 2^(n+1)-1 do
L := A278616T(l) ;
# a := a+ L[1]+L[2]+L[3] ;
a := a+ L[2];
end do:
a ;
end proc: # R. J. Mathar, Dec 02 2016
|
|
|
MATHEMATICA
|
AT[n_] := AT[n] = Module[{an}, If[n == 1, {1, 1, 1}, an = AT[Floor[n/2]]; If[EvenQ[n], {an[[1]] + an[[3]], an[[3]], an[[2]]}, {an[[2]], an[[1]] + an[[3]], an[[1]] } ]]];
a[n_] := a[n] = Module[{a = 0, l, L}, For[l = 2^n, l <= 2^(n + 1) - 1, l++, L = AT[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 22 2017, after R. J. Mathar *)
|
|
|
CROSSREFS
|
Cf. A278612, A278613, A278614, A278615.
Sequence in context: A072632 A001671 A309226 * A278615 A090413 A128105
Adjacent sequences: A278613 A278614 A278615 * A278617 A278618 A278619
|
|
|
KEYWORD
|
nonn,more
|
|
|
AUTHOR
|
Ilya Amburg, Nov 23 2016
|
|
|
EXTENSIONS
|
More terms from R. J. Mathar, Dec 02 2016
|
|
|
STATUS
|
approved
|
| |
|
|
