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A278614 Sum of terms in level n of TRIP -  Stern sequence associated with permutation triple (e,12,12). 5
3, 8, 22, 62, 176, 502, 1434, 4100, 11726, 33542, 95952, 274494, 785266, 2246484, 6426742, 18385646, 52597744, 150471910, 430470890, 1231493604 (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-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-Fran├žois Alcover, Nov 20 2017, after R. J. Mathar *)

CROSSREFS

Cf. A278612, A278613, A278615, A278616.

Sequence in context: A018040 A018041 A073357 * A188464 A298260 A336990

Adjacent sequences:  A278611 A278612 A278613 * A278615 A278616 A278617

KEYWORD

nonn,more

AUTHOR

Ilya Amburg, Nov 23 2016

EXTENSIONS

More terms from R. J. Mathar, Dec 02 2016

STATUS

approved

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Last modified August 17 11:49 EDT 2022. Contains 356189 sequences. (Running on oeis4.)