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A247374 Number of button presses required to try every combination of a binary combination lock with n number buttons. 0
3, 8, 17, 38, 77, 165, 331, 698, 1397, 2921, 5843, 12149, 24299, 50315, 100631, 207698, 415397, 855105, 1710211, 3512801, 7025603, 14403923, 28807847, 58967773, 117935547, 241071395, 482142791, 984343883, 1968687767, 4014934295, 8029868591, 16360277378, 32720554757, 66607912625, 133215825251, 270969218153 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..36.

FORMULA

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.

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

EXAMPLE

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.

All combinations can be tried in 38 presses using the following sequence of presses:

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.

CROSSREFS

Cf. A000079, A014495, A014314.

Sequence in context: A202554 A034481 A295061 * A336512 A046994 A058811

Adjacent sequences:  A247371 A247372 A247373 * A247375 A247376 A247377

KEYWORD

nonn

AUTHOR

Elliott Line, Sep 15 2014

STATUS

approved

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Last modified September 29 22:48 EDT 2022. Contains 357092 sequences. (Running on oeis4.)