A361961 Total semiperimeter of 3-Fuss-Catalan polyominoes of length 3n.

2, 18, 150, 1275, 11033, 96768, 857440, 7658001, 68827440, 621769016, 5640718746, 51355222113, 468976190634, 4293892636600, 39403880112240, 362321464909965, 3337465898598408, 30791007409655928, 284475382593582680, 2631594710532743340, 24372218297220901965, 225958143637966827240

Offset

1,1

Links

Table of n, a(n) for n=1..22.

Toufik Mansour, I. L. Ramirez, Enumerations of polyominoes determined by Fuss-Catalan words, Australas. J. Combin. 81 (3) (2021) 447-457,Table 2.

Formula

Conjecture: D-finite with recurrence 3*n*(396221*n -410120) *(3*n-1) *(3*n+1) *a(n) +4*(-86981513*n^4 +457143117*n^3 -996839467*n^2 +906061905*n -279161658) *a(n-1) +32*(2*n-5) *(4*n-9) *(4*n-7) *(2282347*n -1795413)*a(n-2)=0.

Maple

Per := proc(s, p, n)
    local i, j, a ;
    a := 0 ;
    for i from 0 to n-1 do
    for j from 0 to n-1-i do
        a := a+ (-1)^j*p^(n+1+i+(s+1)*j) *binomial(n-1+i, i)*binomial(n, j)*binomial(n+s*j, n-1-i-j)/(1-p)^(i+j) ;
    end do:
    end do:
    expand(a/n) ;
    factor(%) ;
end proc:
Per1std := proc(s, n)
    local p;
    Per(s, p, n) ;
    diff(%, p) ;
    factor(%) ;
    subs(p=1, %) ;
end proc:
seq(Per1std(3, n), n=1..30) ;

Crossrefs

Cf. A024482 (1-Fuss-Catalan), A078999 (total area), A361960 (2-Fuss-Catalan).

Sequence in context: A356623 A091170 A207319 * A091165 A363568 A191814

Adjacent sequences: A361958 A361959 A361960 * A361962 A361963 A361964

Keyword

nonn,easy

Author

R. J. Mathar, Mar 31 2023

Status

approved