A394572 - OEIS

%I #47 Jun 08 2026 15:31:55

%S 0,1,4,14,36,96,224,544,1216,2816,6144,13824,29696,65536,139264,

%T 303104,638976,1376256,2883584,6160384,12845056,27262976,56623104,

%U 119537664,247463936,520093696,1073741824,2248146944,4630511616,9663676416,19864223744,41339060224,84825604096,176093659136,360777252864,747324309504,1529008357376

%N Minimal value of Sum_{i=1..n} p(i)*p((i mod n)+1), as p ranges over all permutations of powers of 2 {1,2,4,...,2^(n-1)}.

%C The question originated from generalization of the first puzzle 'Low Budget' in the book Mathematical Puzzles and Curiosities.

%D I. David, T. Khovanova, and Y. Shpilman, Mathematical Puzzles and Curiosities, World Scientific, 2026, p.2.

%H Paolo Xausa, <a href="/A394572/b394572.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,4,-8).

%F a(n) = 2^(n-4)*(10*n - 3 - (-1)^n) for n>=1.

%F G.f.: x*(2*x^2+2*x+1)/((2*x+1)*(2*x-1)^2). - _Alois P. Heinz_, May 26 2026

%e For n=4, one permutation that realizes the minimum value is 2,4,1,8. So a(4) = 2*4 + 4*1 + 1*8 + 8*2 = 36. Thus, a(4) = 36.

%t A394572[n_] := Ceiling[2^(n - 4)*(10*n - 3 - (-1)^n)];

%t Array[A394572, 50, 0] (* _Paolo Xausa_, Jun 08 2026 *)

%Y Cf. A026035, A076024, A080675, A110610, A110611, A136412, A395767, A395770.

%K nonn,easy

%O 0,3

%A _Tanya Khovanova_ and PRIMES STEP junior group, May 25 2026