A209288 Main diagonal of the quadruple recurrence x(i,j,k,m) = x(i-1,j,k,m) + x(i,j-1,k,m) + x(i,j,k-1,m) + x(i,j,k,m-1) with x(i,j,k,m) = 1 if 0 in {i,j,k,m}.

1, 4, 196, 22096, 3323092, 574346824, 107697153304, 21304602938056, 4376897152490644, 924871720044550888, 199731547307306769736, 43887077830441507774336, 9780481173520567895278600, 2205358814500087896152369104, 502225405515985555630557626848

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..417

Formula

a(n) = x(n,n,n,n) with x(i,j,k,m) = 1 if 0 in {i,j,k,m} and x(i,j,k,m) = x(i-1,j,k,m) + x(i,j-1,k,m) + x(i,j,k-1,m) + x(i,j,k,m-1) else.

a(n) ~ 2^(8*n-1/2) / (27*(Pi*n)^(3/2)). - Vaclav Kotesovec, Sep 07 2014

Recurrence: 2*(n-2)*(n-1)^3*(3*n - 4)*(3*n - 2)*(10773*n^5 - 127620*n^4 + 601635*n^3 - 1410376*n^2 + 1643420*n - 761136)*a(n) = (n-2)*(50320683*n^10 - 922567239*n^9 + 7517570148*n^8 - 35838081882*n^7 + 110640905811*n^6 - 231017836827*n^5 + 330199460678*n^4 - 318795408964*n^3 + 198794448664*n^2 - 72220580288*n + 11590694016)*a(n-1) - 2*(2*n - 3)*(43339779*n^10 - 841711662*n^9 + 7268645808*n^8 - 36726190830*n^7 + 120139923393*n^6 - 265623988980*n^5 + 401575152460*n^4 - 409434087632*n^3 + 269059885664*n^2 - 102737317696*n + 17273392896)*a(n-2) - 16*(2*n - 5)*(2*n - 3)*(3*n - 8)*(3*n - 7)*(4*n - 11)*(4*n - 9)*(10773*n^5 - 73755*n^4 + 198885*n^3 - 263461*n^2 + 170958*n - 43304)*a(n-3). - Vaclav Kotesovec, Sep 12 2016

Maple

b:= proc() option remember; `if`(args[1]=0, 1,
       add(b(sort(subsop(i=args[i]-1, [args]))[]), i=1..nargs))
    end:
a:= n-> b(n$4):
seq(a(n), n=0..15);  # Alois P. Heinz, Jan 18 2013

Mathematica

b[] = 0; b[args__] := b[args] = If[{args}[[1]] == 0, 1, Sum[b @@ Sort[ ReplacePart[{args}, i -> {args}[[i]] - 1]], {i, 1, Length[{args}]}]];
a[n_] := b @@ Table[n, 4];
Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Jun 03 2018, after Alois P. Heinz *)

Crossrefs

Cf. A209245.

Column k=4 of A210472. - Alois P. Heinz, Jan 23 2013

Sequence in context: A221197 A180991 A279803 * A263422 A065246 A297061

Adjacent sequences: A209285 A209286 A209287 * A209289 A209290 A209291

Keyword

nonn

Author

Jon Perry, Jan 16 2013

Status

approved