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

Author

N. J. A. Sloane, Apr 09 2016

Keywords

• nonn

Links

• 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.

Crossrefs

Cf. A019774, A093302.

Programs

GAP

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

Maple

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

Mathematica

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

PARI

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

PARI

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

Formula

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)

Extensions

More terms from Gheorghe Coserea, Apr 25 2016