A337999 a(n) = 2^floor((2-n)/2)*Sum_{0 <= k <= n and A337966(n, k) > 0} A173018(n, k).

2, 2, 0, 0, 11, 33, 29, 60, 3905, 19524, 62879, 275436, 10187165, 71191608, 481719419, 3211782240, 101121160145, 904977244224, 10099756468559, 89733565369536, 2746252055597525, 29900664884062848, 479479605967022099, 5296351543857279360, 166991194742961246905

Offset

0,1

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

(a(n) - A338000(n))/2 = (-1)^floor(n/2)*A000111(n).

(-1)^floor(n/2)*(a(n) - A338000(n)) = A001250(n) for n >= 2.

Example

Row 6 of A337967 is: 1, 57, -302, -302, 57, 1, 0. The sum of positive terms is 2*(1 + 57) = 116. Thus a(6) = 116/4 = 29.

Maple

A337999 := n -> add(`if`(A337966(n, k)>0, A173018(n, k), 0), k=0..n)/2^floor((n-2)/2): seq(A337999(n), n=0..24);

Crossrefs

Cf. A337966, A337967, A173018, A338000, A000111, A001250.

Sequence in context: A230592 A282699 A182107 * A037224 A122670 A352661

Adjacent sequences: A337996 A337997 A337998 * A338000 A338001 A338002

Keyword

nonn

Author

Peter Luschny, Oct 06 2020

Status

approved