A042971 a(n) = (C(2n, n)/2 - (2^(n-1) + ((n+1) mod 2)*C(n-1, n/2-1)))/2.

0, 0, 3, 12, 55, 210, 826, 3136, 12027, 45870, 175846, 674784, 2598102, 10024196, 38771188, 150250496, 583368787, 2268706134, 8836184878, 34461323872, 134563944322, 526023515996, 2058355584748, 8061896050432, 31602643220830, 123979613859660, 486734822857596

Offset

1,3

Comments

Number of distinct asymmetric staircase walks connecting opposite corners of a square grid of side n > 1. - Christian Barrientos, Nov 25 2018

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Example

U = up, R = right Example of asymmetric staircase walk: URURUURR. - Christian Barrientos, Nov 29 2018

Mathematica

Table[Binomial[2n, n]/2-(2^(n-1)+Mod[n+1, 2]Binomial[n-1, n/2-1]), {n, 30}]/2

Prog

(PARI) a(n) = (binomial(2*n, n)/2 - (2^(n-1) + if (((n+1) % 2), binomial( n-1, n/2-1))))/2; \\ Michel Marcus, Nov 25 2018
(Magma) [(Binomial(2*n, n) -(2^n +(1+(-1)^n)*Binomial(n-1, Floor(n/2)-1) ))/4: n in [1..30]]; // G. C. Greubel, Feb 17 2019
(Sage) [(binomial(2*n, n) -(2^n + (1+(-1)^n)*binomial(n-1, floor(n/2)-1)))/4 for n in (1..30)] # G. C. Greubel, Feb 17 2019

Crossrefs

Cf. A027306 (for symmetric staircase walks).

Sequence in context: A052673 A180589 A370937 * A256142 A024038 A371429

Adjacent sequences: A042968 A042969 A042970 * A042972 A042973 A042974

Keyword

nonn

Author

Wouter Meeussen

Status

approved