A378117 Lexicographically earliest sequence of nonnegative integers a(0), a(1), ..., such that a(n) is the number of pairs of adjacent terms whose sum is n.

0, 1, 1, 2, 1, 3, 2, 3, 2, 4, 2, 5, 2, 5, 3, 5, 4, 5, 4, 5, 5, 5, 6, 5, 6, 5, 6, 6, 6, 7, 6, 7, 6, 7, 7, 7, 7, 8, 7, 8, 7, 8, 8, 8, 8, 8, 9, 8, 9, 8, 9, 9, 9, 9, 9, 10, 9, 10, 9, 10, 10, 10, 10, 10, 10, 11, 10, 11, 10, 11, 11, 11, 11, 11, 11, 11, 12, 11, 12

Offset

0,4

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10032

Rémy Sigrist, Colored scatterplot of the first 65000 terms (where the color denotes the parity of n)

Rémy Sigrist, C++ program

Example

We can take a(0) = 0.
We cannot take a(1) = 0 as there are no pairs of consecutive terms summing to 0.
We can take a(1) = 1.
We cannot take a(2) = 0 as we already have one pair of consecutive terms summing to 1.
We can take a(2) = 1.
We cannot take a(3) = 0 as we already have one pair of consecutive terms summing to 1.
We cannot take a(3) = 1 as we already have one pair of consecutive terms summing to 2.
We can take a(3) = 2.

Prog

(C++) // See Links section.

Crossrefs

Cf. A001462, A307707.

Sequence in context: A237127 A262746 A007828 * A070804 A303429 A303656

Adjacent sequences: A378113 A378114 A378115 * A378118 A378120 A378121

Keyword

nonn,new

Author

Rémy Sigrist and N. J. A. Sloane, Nov 17 2024

Status

approved