A361962 Total number of 2-Fuss-skew paths of semilength n.

2, 14, 118, 1114, 11306, 120534, 1331374, 15103410, 174935250, 2060200670, 24595806758, 296993911690, 3620853162618, 44509749949094, 551065497319006, 6865424096224610, 86005892134892962, 1082728353985352878, 13690429445139361494, 173792202854983764666, 2214092570427696031434

Offset

1,1

Links

Table of n, a(n) for n=1..21.

Toufik Mansour, Jose Luis Ramirez, Enumration of Fuss-skew paths, Ann. Math. Inform. 55 (2022) 125-136, table 1, l=2.

Formula

D-finite with recurrence 10*n*(2*n+1)*a(n) +3*(-121*n^2+155*n-46)*a(n-1) +3*(431*n^2-1579*n+1418)*a(n-2) -(961*n-2440) *(n-3) *a(n-3) -85*(n-3)*(n-4)*a(n-4)=0

Maple

FussSkew := proc(l, n)
    local a, j, k;
    a := 0 ;
    for j from 0 to n do
        a := a+sum( binomial(n, j) *binomial(j, k) *binomial(n*(l-1), n-2*j+k-1)
        * 3^k*2^(n*(l-2)+2*j-k+1), k=0..j) ;
    end do:
    a/n ;
end proc:
seq(FussSkew(2, n), n=1..40) ;

Crossrefs

Cf. A002212 (1-Fuss-skew), A361963 (3-Fuss-skew)

Sequence in context: A277467 A208393 A370671 * A192457 A351856 A155728

Adjacent sequences: A361959 A361960 A361961 * A361963 A361964 A361965

Keyword

nonn,easy

Author

R. J. Mathar, Mar 31 2023

Status

approved