cp's OEIS Frontend

A247374 Number of button presses required to try every combination of a binary combination lock with n number buttons.

%I A247374 #14 Jan 30 2020 21:58:01
%S A247374 3,8,17,38,77,165,331,698,1397,2921,5843,12149,24299,50315,100631,
%T A247374 207698,415397,855105,1710211,3512801,7025603,14403923,28807847,
%U A247374 58967773,117935547,241071395,482142791,984343883,1968687767,4014934295,8029868591,16360277378,32720554757,66607912625,133215825251,270969218153
%N A247374 Number of button presses required to try every combination of a binary combination lock with n number buttons.
%C A247374 This type of lock is quite common in the real world. The lock has typically 13 'number' buttons (actually 0 1 2 3 4 5 6 7 8 9 X Y Z), plus a C (for clear) button, and a knob to turn to 'try' the combination. The way it functions is that the unlocking code is an n-digit binary number. By pressing one of the number buttons, you change the corresponding digit from 0 to 1. Pressing C reverts all digits to 0.
%F A247374 a(n) = A000079(n) + A014495(n) + A014314(n). A000079 is how many times the 'try' button (or knob) is pressed. A014495 is how many times the C (clear) button is pressed. A014314 is how many times the number buttons are pressed.
%F A247374 Conjectured to be D-finite with recurrence: n*a(n) +2*(-2*n+1)*a(n-1) +(n-2)*a(n-2) +2*(7*n-10)*a(n-3) +4*(-5*n+11)*a(n-4) +8*(n-3)*a(n-5)=0. - _R. J. Mathar_, Nov 19 2019
%e A247374 A lock with four number buttons (plus try and clear) would have 16 combinations to try, namely 0000, 0001, 0010, 0011, 0100, 0101, 0110, 0111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111.
%e A247374 All combinations can be tried in 38 presses using the following sequence of presses:
%e A247374 T 1 T 2 T 3 T 4 T C 2 T 3 T 4 T C 3 T 4 T 1 T C 4 T 1 T 2 T C 1 3 T C 2 4 T. The T (tries) will attempt the combinations in the following order: 0000, 1000, 1100, 1110, 1111, 0100, 0110, 0111, 0010, 0011, 1011, 0001, 1001, 1101, 1010, 0101.
%Y A247374 Cf. A000079, A014495, A014314.
%K A247374 nonn
%O A247374 1,1
%A A247374 _Elliott Line_, Sep 15 2014