A365644 -id:A365644 - cp's OEIS frontend

A365645 a(n) = n(1 + n)(10^n - 1)/18.

0, 1, 33, 666, 11110, 166665, 2333331, 31111108, 399999996, 4999999995, 61111111105, 733333333326, 8666666666658, 101111111111101, 1166666666666655, 13333333333333320, 151111111111111096, 1699999999999999983, 18999999999999999981, 211111111111111111090, 2333333333333333333310

Offset: 0

Stefano Spezia, Sep 14 2023

Stefano Spezia, Table of n, a(n) for n = 0..990
Index entries for linear recurrences with constant coefficients, signature (33,-393,1991,-3930,3300,-1000).

Antidiagonal sums of A365644.

Mathematica
```
Table[n(1+n)(10^n-1)/18,{n,0,20}]
```

O.g.f.: x*(1 - 30*x^2 + 110*x^3)/((1 - x)^3*(1 - 10*x)^3).
E.g.f.: exp(x)*x*(20*exp(9*x)*(1 + 5*x) - 2 - x)/18.
a(n) = 33*a(n-1) - 393*a(n-2) + 1991*a(n-3) - 3930*a(n-4) + 3300*a(n-5) - 1000*a(n-6) for n > 5.

A365646 a(n) is the permanent of the n X n matrix M(n) whose generic M[i, j] = j*(10^i - 1)/9 with 1 <= i, j <= n.

Original entry on oeis.org

1, 1, 44, 43956, 781361856, 217042789550400, 868170290030441798400, 47267044397174696636039097600, 33612120124091913005718848881499750400, 302509080814318135934642422882028113666502246400, 33612120087118580872578956587618207930922159448149975040000

Offset: 0

Stefano Spezia, Sep 14 2023

nonn

For n > 1, the matrix M(n) is singular.

			a(3) = 43956:
  [  1,   2,   3]
  [ 11,  22,  33]
  [111, 222, 333]

Cf. A365644.

M[i_,j_]:=j(10^i-1)/9; Join[{1},Table[Permanent[Table[M[i,j],{i,n},{j,n}]],{n,10}]]

a(n) = matpermanent(matrix(n,n,i,j,j*(10^i - 1)/9)); \\ Michel Marcus, Sep 17 2023

cp's OEIS Frontend

A365645 a(n) = n(1 + n)(10^n - 1)/18.

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A365646 a(n) is the permanent of the n X n matrix M(n) whose generic M[i, j] = j*(10^i - 1)/9 with 1 <= i, j <= n.

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cp's OEIS Frontend

A365645 a(n) = n*(1 + n)*(10^n - 1)/18.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

A365646 a(n) is the permanent of the n X n matrix M(n) whose generic M[i, j] = j*(10^i - 1)/9 with 1 <= i, j <= n.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

PARI

A365645 a(n) = n(1 + n)(10^n - 1)/18.