A244475 -id:A244475 - cp's OEIS frontend

A244472 2nd-largest term in n-th row of Stern's diatomic triangle A002487.

1, 2, 4, 7, 12, 19, 31, 50, 81, 131, 212, 343, 555, 898, 1453, 2351, 3804, 6155, 9959, 16114, 26073, 42187, 68260, 110447, 178707, 289154, 467861, 757015, 1224876, 1981891, 3206767, 5188658, 8395425, 13584083, 21979508, 35563591, 57543099

Offset: 1

N. J. A. Sloane, Jul 01 2014

Colin Barker, Table of n, a(n) for n = 1..1000
Jennifer Lansing, Largest Values for the Stern Sequence, J. Integer Seqs., 17 (2014), #14.7.5.
Index entries for linear recurrences with constant coefficients, signature (1,1).

Cf. A002487, A013655, A100545 (bisection).

Cf. A244473, A244474, A244475, A244476.

I:=[1, 2, 4, 7, 12]; [n le 5 select I[n] else Self(n-1)+Self(n-2): n in [1..40]]; // Wesley Ivan Hurt, Jul 10 2015

A244472 := proc(n)
    if n < 4 then
        op(n,[1,2,4]) ;
    else
        combinat[fibonacci](n+2)-combinat[fibonacci](n-3) ;
    end if;
end proc:
seq(A244472(n),n=1..50) ; # R. J. Mathar, Jul 05 2014

CoefficientList[Series[-(x^4 + x^3 + x^2 + x + 1)/(x^2 + x - 1), {x, 0, 50}], x] (* Wesley Ivan Hurt, Jul 10 2015 *)
Join[{1, 2, 4}, LinearRecurrence[{1, 1}, {7, 12}, 50]] (* Vincenzo Librandi, Jul 11 2015 *)

Vec(-x*(x^4+x^3+x^2+x+1)/(x^2+x-1) + O(x^100)) \\ Colin Barker, Jul 10 2015

a(n) = A013655(n-1), n>3.
a(n) = a(n-1)+a(n-2), n>5. - Colin Barker, Jul 10 2015
G.f.: -x*(x^4+x^3+x^2+x+1) / (x^2+x-1). - Colin Barker, Jul 10 2015

A244476 6th-largest term in n-th row of Stern's diatomic triangle A002487.

Original entry on oeis.org

2, 8, 15, 26, 45, 75, 121, 199, 322, 542, 877, 1427, 2309, 3739, 6050, 9790, 15841, 25632, 41473, 67105, 108578, 175683, 284261, 459944, 744205, 1204149, 1948354, 3152503, 5100857, 8253360

Offset: 4

N. J. A. Sloane, Jul 01 2014

Jennifer Lansing, Largest Values for the Stern Sequence, Journal of Integer Sequences, Vol. 17 (2014), Article 14.7.5.

Cf. A002487, A244472, A244473, A244474, A244475.

from functools import reduce
from itertools import product
def A244476(n): return sorted(set(sum(reduce(lambda x,y:(x[0],x[0]+x[1]) if y else (x[0]+x[1],x[1]),k,(1,0))) for k in product((False,True),repeat=n)),reverse=True)[5] # Chai Wah Wu, Jun 19 2022

a(24)-a(33) from Chai Wah Wu, Jun 19 2022

A244474 4th-largest term in n-th row of Stern's diatomic triangle A002487.

Original entry on oeis.org

2, 4, 10, 17, 29, 47, 79, 128, 208, 337, 546, 883, 1429, 2312, 3741, 6053, 9794, 15847, 25641, 41488, 67129, 108617

Offset: 3

N. J. A. Sloane, Jul 01 2014

Jennifer Lansing, Largest Values for the Stern Sequence, J. Integer Seqs., 17 (2014), #14.7.5.

Cf. A002487, A244472, A244473, A244475, A244476.

A002487 := proc(n,k)
    option remember;
    if k =0 then
        1;
    elif k = 2^n-1 then
        n+1 ;
    elif type(k,'even') then
        procname(n-1,k/2) ;
    else
        procname(n-1,(k-1)/2)+procname(n-1,(k+1)/2) ;
    end if;
end proc:
A244474 := proc(n)
    {seq(A002487(n,k),k=0..2^n-1)} ;
    sort(%) ;
    op(-4,%) ;
end proc:
for n from 3 do
    print(A244474(n)) ;
od: # R. J. Mathar, Oct 25 2014

s[n_] := s[n] = Switch[n, 0, 0, 1, 1, _, If[EvenQ[n], s[n/2], s[(n - 1)/2] + s[(n - 1)/2 + 1]]];
T = Table[s[n], {n, 0, 2^25}] // Flatten // SplitBy[#, If[# == 1, 1, 0]&]& // DeleteCases[#, {1}]&;
Union[#][[-4]]& /@ T[[5 ;;]] (* Jean-François Alcover, Mar 12 2023 *)

from itertools import product
from functools import reduce
def A244474(n): return sorted(set(sum(reduce(lambda x,y:(x[0],x[0]+x[1]) if y else (x[0]+x[1],x[1]),k,(1,0))) for k in product((False,True),repeat=n)),reverse=True)[3] # Chai Wah Wu, Jun 20 2022

G.f.: (-2-2*x-4*x^2-3*x^3-2*x^4-x^5-3*x^6-2*x^7-x^8-x^9-x^10)/(-1+x+x^2) (conjectured) - Jean-François Alcover, Mar 12 2023

a(24) from Jean-François Alcover, Mar 12 2023

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A244472 2nd-largest term in n-th row of Stern's diatomic triangle A002487.

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A244476 6th-largest term in n-th row of Stern's diatomic triangle A002487.

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A244474 4th-largest term in n-th row of Stern's diatomic triangle A002487.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

Python

Formula

Extensions