A338000 a(n) = 2^floor((2-n)/2)*Sum_{0 <= k <= n and A337966(n, k) < 0} A173018(n, k).

0, 0, 2, 4, 1, 1, 151, 604, 1135, 3652, 163921, 983020, 4781635, 26455096, 880441381, 7019296864, 62338135855, 485246558272, 14909515819441, 147911335595200, 2005509679122475, 19997668777814656, 618177354753297901, 7327199316870984064, 135962126415847073095

Offset

0,3

Comments

The two sequences A337999 and A338000 represent the number of alternating permutations of order n as the difference between the greater and the smaller of the two absolute values (for n >= 2).

Links

Table of n, a(n) for n=0..24.

Formula

(A337999(n) - a(n))/2 = (-1)^floor(n/2)*A000111(n).

(-1)^floor(n/2)*(A337999(n) - a(n)) = A001250(n) for n >= 2.

Example

Row 6 of A337967 is: 1, 57, -302, -302, 57, 1, 0. The sum of negative terms is 2*302 = 604. Thus a(6) = 604/4 = 151.

Maple

A338000 := n -> add(`if`(A337966(n, k)<0, A173018(n, k), 0), k=0..n)/2^floor((n-2)/2): seq(A338000(n), n=0..24);

Crossrefs

Cf. A337966, A337967, A173018, A337999, A000111, A001250.

Sequence in context: A197489 A297966 A103161 * A030420 A133902 A265823

Adjacent sequences: A337997 A337998 A337999 * A338001 A338002 A338003

Keyword

nonn

Author

Peter Luschny, Oct 06 2020

Status

approved