A083080 -id:A083080 - cp's OEIS frontend

A083075 Square array read by antidiagonals: T(n,k) = (k(2k+3)^n + 1)/(k+1).

1, 1, 1, 1, 3, 1, 1, 5, 13, 1, 1, 7, 33, 63, 1, 1, 9, 61, 229, 313, 1, 1, 11, 97, 547, 1601, 1563, 1, 1, 13, 141, 1065, 4921, 11205, 7813, 1, 1, 15, 193, 1831, 11713, 44287, 78433, 39063, 1, 1, 17, 253, 2893, 23801, 128841, 398581, 549029, 195313, 1, 1, 19, 321

Offset: 0

Paul Barry, Apr 23 2003

			Array begins:
  1     1     1     1     1 ...
  1     3    13    63   313 ...
  1     5    33   229  1601 ...
  1     7    61   547  4921 ...
  1     9    97  1065 11713 ...
  ...

Nathaniel Johnston, Antidiagonals 0..100, flattened

Rows include A034478, A083076, A066443, A083077, A083078.
Columns include odds, A082109, A083079.
Diagonals include A083079, A083080, A083081, A083082.

T := proc(n,k) return (k*(2*k+3)^n+1)/(k+1): end: seq(seq(T(k,n-k),k=0..n),n=0..10); # Nathaniel Johnston, Jun 26 2011

A083082 First subdiagonal of number array A083075.

Original entry on oeis.org

1, 5, 61, 1065, 23801, 650893, 21120373, 794552657, 34040573425, 1637411510421, 87420145670573, 5131440522974329, 328542298690792681, 22789709877615373085, 1702810951672313083621, 136361486383932674632353

Offset: 0

Paul Barry, Apr 23 2003

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Cf. A083080, A083083.

[((n+1)*(2*n+5)^n+1)/(n+2): n in [0..20]]; // Vincenzo Librandi, Nov 12 2011

Table[((n+1)(2n+5)^n+1)/(n+2),{n,0,20}] (* Harvey P. Dale, Oct 06 2019 *)

a(n) = ((n+1)*(2n+5)^n + 1)/(n+2).

A083081 First superdiagonal of number array A083075.

Original entry on oeis.org

1, 13, 229, 4921, 128841, 4022341, 146450893, 6103787761, 286833509137, 15011892880381, 866190689012661, 54637591044108073, 3740820141248285785, 276304073198956644661, 21900911192388373534621

Offset: 1

Paul Barry, Apr 23 2003

Vincenzo Librandi, Table of n, a(n) for n = 1..300

Cf. A083080, A083082.

[((n-1)*(2*n+1)^n+1)/n: n in [1..20]]; // Vincenzo Librandi, Nov 12 2011

a(n) = ((n-1)*(2n+1)^n + 1)/n.

cp's OEIS Frontend

A083075 Square array read by antidiagonals: T(n,k) = (k(2k+3)^n + 1)/(k+1).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

A083082 First subdiagonal of number array A083075.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

Formula

A083081 First superdiagonal of number array A083075.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Formula

cp's OEIS Frontend

A083075 Square array read by antidiagonals: T(n,k) = (k*(2*k+3)^n + 1)/(k+1).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

A083082 First subdiagonal of number array A083075.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

Formula

A083081 First superdiagonal of number array A083075.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Formula

A083075 Square array read by antidiagonals: T(n,k) = (k(2k+3)^n + 1)/(k+1).