A336653 First differences of A271215.

-1, 1, 3, 20, 160, 1727, 22341, 337947, 5799881, 111180832, 2352448424, 54449597409, 1368516031855, 37118127188225, 1080644471447419, 33614180067524196, 1112586937337720904, 39043623554061199807, 1448021297870473796645, 56592256120004219495755, 2324706946641972649074513

Offset: 1

Author

Michel Marcus, Jul 28 2020

Keywords

• sign

Comments

a(n) is the number of epsilon-paths of the n-cube for n>=2.

Links

• Kristin DeSplinter, Satyan L. Devadoss, Jordan Readyhough, and Bryce Wimberly, Unfolding cubes: nets, packings, partitions, chords, arXiv:2007.13266 [math.CO], 2020. See Table 1 p. 15.

Crossrefs

Cf. A000806, A271215.

Programs

PARI

f(n) = sum(k=0, n, (2*n-k)! / (k! * (n-k)!) * (-1/2)^(n-k) ); \\ A000806
lista(nn) = {my(va = vector(nn)); va[1] = 1; va[2] = 0; va[3] = 1; va[4] = 3; va[5] = 12; for (n=5, nn-1, va[n+1] = 2*va[n] + (2*n-3)*va[n-1] - (2*n-5)*va[n-2] + 2*va[n-3] - va[n-4];); my(w=vector(nn-1, n, (va[n] + abs(f(n-1)))/2)); vector(#w-1, k, w[k+1] - w[k]);} \\ Michel Marcus, Jul 28 2020

Formula

a(n) = A271215(n) - A271215(n-1).