A093302 -id:A093302 - cp's OEIS frontend

A271476 Total number of burnt pancakes flipped using the Min-bar(n) greedy algorithm.

1, 10, 75, 628, 6325, 75966, 1063615, 17017960, 306323433, 6126468850, 134782314931, 3234775558620, 84104164524445, 2354916606684838, 70647498200545575, 2260719942417458896, 76864478042193603025, 2767121209518969709530, 105150605961720848962843, 4206024238468833958514500

Offset: 1

N. J. A. Sloane, Apr 09 2016

nonn

Gheorghe Coserea, Table of n, a(n) for n = 1..128
J. Sawada, A. Williams, Successor rules for flipping pancakes and burnt pancakes, Preprint, Theoretical Computer Science, Volume 609, Part 1, 4 January 2016, Pages 60-75.

Cf. A019774, A093302.

List([1..20],n->-n+2^n*Factorial(n)*Sum([0..n-1],k->1/(2^k*Factorial(k)))); # Muniru A Asiru, Aug 02 2018

seq(coeff(series(factorial(n)*exp(x)*(x+2*x^2)/(1-2*x), x,n+1),x,n),n=1..20); # Muniru A Asiru, Aug 02 2018

Table[2^n*n! Sum[1/(2^k*k!), {k, 0, n - 1}] - n, {n, 20}] (* Michael De Vlieger, May 25 2016 *)

a(n) = 2^n * n! * sum(k=0, n-1, 1/(2^k*k!)) - n;
vector(20, n, a(n))  \\ Gheorghe Coserea, Apr 25 2016

x='x+O('x^99); Vec(serlaplace((x+2*x^2)/(1-2*x)*exp(x))) \\ Altug Alkan, Aug 01 2018

a(n) = -n + 2^n * n! * Sum_{k=0..n-1} 1/(2^k*k!). (see Sawada link) - Gheorghe Coserea, Apr 25 2016
From Altug Alkan, Aug 01 2018: (Start)
a(n) = A093302(n)/2 for n >= 1.
a(n) = floor(e^(1/2)*n!*2^n)-n-1.
E.g.f.: exp(x)*(x+2*x^2)/(1-2*x). (End)

More terms from Gheorghe Coserea, Apr 25 2016

A339516 a(n+1) = (a(n) - 2(n-1)) (2*n-1), where a(1)=1.

Original entry on oeis.org

1, 1, -3, -35, -287, -2655, -29315, -381251, -5718975, -97222847, -1847234435, -38791923555, -892214242271, -22305356057375, -602244613549827, -17465093792945795, -541417907581320575, -17866790950183580031, -625337683256425302275, -23137494280487736185507

Offset: 1

Kamil Zabkiewicz, Dec 07 2020

sign

The sequence appears when computing constants that encode all odd numbers starting from 3, then from 5, then from 7, etc. The general formula of the constant is a(n) + (2n-1)!!*sqrt(2*Pi*e)*erf(1/sqrt(2)), where n>0. For more information on how to generate the constant please watch the Grime-Haran Numberphile video.

James Grime and Brady Haran, 2.920050977316, Numberphile video, Nov 26 2020.

Cf. A047907, A093302, A001147.

A339516 := proc(n)
    option remember ;
    if n = 1 then
        1;
    else
        (2*n-3)*(procname(n-1)-2*(n-2)) ;
    end if;
end proc:
seq(A339516(n),n=1..30) ; # R. J. Mathar, Aug 24 2022

a[1]=1;a[n_]:=(a[n-1]-2(n-2))(2n-3); Array[a,20] (* Stefano Spezia, Dec 08 2020 *)
nxt[{n_,a_}]:={n+1,(a-2n)(2n+1)}; Join[{1},NestList[nxt,{1,1},20][[;;,2]]] (* Harvey P. Dale, Aug 25 2024 *)

#generate first 50 numbers of the sequence
cnt = 50
i=0
seq = list()
seq.append(1)
i=1
while (i

Homogeneous recurrence: (-2*n+9)*a(n-4) + (6*n-20)*a(n-3) + (-6*n+12)*a(n-2) + 2*n*a(n-1) - a(n) = 0 with a(1)=a(2)=1, a(3)=-3, a(4)=-35. - Georg Fischer, Sep 01 2022

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A271476 Total number of burnt pancakes flipped using the Min-bar(n) greedy algorithm.

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A339516 a(n+1) = (a(n) - 2(n-1)) (2*n-1), where a(1)=1.

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cp's OEIS Frontend

A271476 Total number of burnt pancakes flipped using the Min-bar(n) greedy algorithm.

Views

Author

Keywords

Links

Crossrefs

Programs

GAP

Maple

Mathematica

PARI

PARI

Formula

Extensions

A339516 a(n+1) = (a(n) - 2*(n-1)) * (2*n-1), where a(1)=1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

Python

Formula

A339516 a(n+1) = (a(n) - 2(n-1)) (2*n-1), where a(1)=1.