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

1,2

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.

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)

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 *)

Prog

(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
(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

Crossrefs

Cf. A019774, A093302.

Sequence in context: A081017 A238987 A357480 * A025015 A228416 A049392

Adjacent sequences: A271473 A271474 A271475 * A271477 A271478 A271479

Keyword

nonn

Author

N. J. A. Sloane, Apr 09 2016

Extensions

More terms from Gheorghe Coserea, Apr 25 2016

Status

approved