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Omni-MATH / Find, with proof, the number of positive integers whose base- n representation consists of distinct digits with the property that, except for the leftmost digit, every digit differ…

Problem

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problem

Find, with proof, the number of positive integers whose base- nn representation consists of distinct digits with the property that, except for the leftmost digit, every digit differs by ±1\pm 1 from some digit further to the left. (Your answer should be an explicit function of nn in simplest form.)
Plain-text mathematical notation (without MathML)
Find, with proof, the number of positive integers whose base- n representation consists of distinct digits with the property that, except for the leftmost digit, every digit differs by ±1 from some digit further to the left.  (Your answer should be an explicit function of n in simplest form.)
Original LaTeX notation
Find, with proof, the number of positive integers whose base- $n$ representation consists of distinct digits with the property that, except for the leftmost digit, every digit differs by $\pm 1$ from some digit further to the left.  (Your answer should be an explicit function of $n$ in simplest form.)

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Source and history

task_id
57c1c491-7b1e-5bea-b2ae-dbbded31a5fb
task_key
test--57c1c491-7b1e-5bea-b2ae-dbbded31a5fb
task_revision_id
1
config / split
/ test

Official source

initial import