A302181 Number of 3D walks of type abb.

1, 5, 62, 1065, 21714, 492366, 12004740, 308559537, 8255788970, 227976044010, 6457854821340, 186814834574550, 5500292590186380, 164387681345290500, 4976887208815547640, 152378485941172462785, 4711642301137121933850, 146964278352052950118770, 4619875954522866283392300

Offset: 0

Author

N. J. A. Sloane, Apr 09 2018

Keywords

• nonn
• walk

Comments

See Dershowitz (2017) for precise definition.

Links

• Nachum Dershowitz, Touchard's Drunkard, Journal of Integer Sequences, Vol. 20 (2017), #17.1.5.

Crossrefs

Cf. A000108, A000984, A002212, A002896, A005572, A026375, A064037, A081671, A138547, A145847, A145867, A150500, A202814.

Cf. A005558, A126869.

Programs

Maple

C := n-> binomial(2*n, n)/(n+1): # Catalan numbers
A302181 := n-> add(binomial(2*n, k)*C(iquo(k+1, 2))*C(iquo(k, 2))*(2*iquo(k, 2)+1)*add((-1)^(k+j)*binomial(2*n-k, iquo(j,2)), j=0..2*n-k), k=0..2*n): seq(A302181(n), n = 0 .. 18); # Mélika Tebni, Nov 06 2024

Formula

a(n) = Sum_{k=0..2*n} binomial(2*n, k) * A005558(k) * A126869(2*n-k). - Mélika Tebni, Nov 06 2024

Extensions

a(8)-a(18) from Nachum Dershowitz, Aug 03 2020