cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

User: Ilya Amburg

Ilya Amburg's wiki page.

Ilya Amburg has authored 5 sequences.

A278616 Sum of terms in level n of TRIP - Stern sequence associated with permutation triple (e,13,132).

Original entry on oeis.org

3, 8, 21, 56, 148, 393, 1041, 2761, 7318, 19403, 51436, 136366, 361513, 958413, 2540831, 6735996, 17857733, 47342548, 125509476, 332737401
Offset: 0

Views

Author

Ilya Amburg, Nov 23 2016

Keywords

Links

Crossrefs

Cf. A278612, A278613, A278614, A278615.

Programs

  • 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 *)

Formula

Conjecture: G.f.: ( -3-5*x-x^2 ) / ( -1+x+4*x^2+x^3 ). - R. J. Mathar, Dec 02 2016

Extensions

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

A278612 Sum of terms in level n of TRIP - Stern sequence associated with permutation triple (e, e, e).

Original entry on oeis.org

3, 8, 22, 60, 162, 436, 1174, 3164, 8530, 22996, 61990, 167100, 450434, 1214196, 3273014, 8822812, 23782962, 64109844, 172815814, 465845884, 1255743842, 3385009204, 9124701142, 24596733916, 66303466770, 178729002068, 481785610086, 1298711297084, 3500833146178, 9436918539636, 25438353615990
Offset: 0

Views

Author

Ilya Amburg, Nov 23 2016

Keywords

Links

Crossrefs

Cf. A278613, A278614, A278615, A278616.

Programs

  • PARI
    Vec((3 - 4*x + 5*x^2) / (1 - 4*x + 5*x^2 - 4*x^3) + O(x^40)) \\ Colin Barker, Jan 09 2018

Formula

a(n) = A271896(n) + A271897(n) + A271898(n). - R. J. Mathar, Dec 02 2016
From Colin Barker, Jan 09 2018: (Start)
G.f.: (3 - 4*x + 5*x^2) / (1 - 4*x + 5*x^2 - 4*x^3).
a(n) = 4*a(n-1) - 5*a(n-2) + 4*a(n-3) for n>2.
(End)

A278613 Sum of terms in level n of TRIP - Stern sequence associated with permutation triple (e,e,132).

Original entry on oeis.org

3, 8, 21, 55, 145, 381, 1001, 2633, 6921, 18193, 47833, 125745, 330569, 869057, 2284665, 6006193, 15789865, 41510241, 109127129, 286886801
Offset: 0

Views

Author

Ilya Amburg, Nov 23 2016

Keywords

Links

Crossrefs

Cf. A278612, A278614, A278615, A278616.

Formula

Conjecture: G.f.: ( -3-5*x-7*x^2 ) / ( -1+x+2*x^2+6*x^3 ). - R. J. Mathar, Dec 02 2016

Extensions

New offset and a(10)-a(19) from R. J. Mathar, Dec 02 2016

A278614 Sum of terms in level n of TRIP - Stern sequence associated with permutation triple (e,12,12).

Original entry on oeis.org

3, 8, 22, 62, 176, 502, 1434, 4100, 11726, 33542, 95952, 274494, 785266, 2246484, 6426742, 18385646, 52597744, 150471910, 430470890, 1231493604
Offset: 0

Views

Author

Ilya Amburg, Nov 23 2016

Keywords

Links

Crossrefs

Cf. A278612, A278613, A278615, A278616.

Programs

  • 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 *)

Formula

Conjecture: G.f.: ( 3-x-5*x^2 ) / ( 1-3*x-x^2+4*x^3 ). - R. J. Mathar, Dec 02 2016

Extensions

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

A278615 Sum of terms in level n of TRIP - Stern sequence associated with permutation triple (e,13,23).

Original entry on oeis.org

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

Views

Author

Ilya Amburg, Nov 23 2016

Keywords

Links

Crossrefs

Cf. A271893, A278612, A278613, A278614, A278616.

Programs

  • 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. *)

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

Extensions

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

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