A083082 -id:A083082 - 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

A083080 Main diagonal of number array A083075.

Original entry on oeis.org

1, 3, 33, 547, 11713, 309411, 9763393, 359046339, 15096500481, 714852041923, 37660464739681, 2185503641764323, 138548894120306881, 9527726662032987747, 706481006206076565633, 56192761405186331759491

Offset: 0

Paul Barry, Apr 23 2003

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

Cf. A083081, A083082.

[(n*(2*n+3)^n+1)/(n+1): n in [0..20]]; // Vincenzo Librandi, Nov 12 2011

a(n) = (n*(2n+3)^n + 1)/(n+1).

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.

A083083 A diagonal of number array A083075.

Original entry on oeis.org

1, 7, 97, 1831, 43393, 1242375, 41818561, 1620979687, 71191804801, 3496805826823, 190053352702753, 11329044782441127, 735151931535979777, 51600331868857972231, 3896042468112362132353, 314921475287825567805799

Offset: 0

Paul Barry, Apr 23 2003

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

Cf. A083082, A083084.

[((n+2)*(2*n+7)^n+1)/(n+3): n in [0..20]]; // Vincenzo Librandi, Nov 12 2011

Table[((n+2)(2n+7)^n+1)/(n+3),{n,0,20}] (* Harvey P. Dale, Nov 18 2021 *)

a(n) = ((n+2)*(2n+7)^n + 1)/(n+3).

A083084 A diagonal of number array A083075.

Original entry on oeis.org

1, 9, 141, 2893, 73081, 2200977, 77189509, 3095295861, 139872233073, 7039013063065, 390656716635901, 23714578436644509, 1563646420268423401, 111315499088924632353, 8511391223995285616373, 695805743909499121660357

Offset: 0

Paul Barry, Apr 23 2003

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

Cf. A083083, A083082.

[((n+3)*(2*n+9)^n+1)/(n+4): n in [0..20]]; // Vincenzo Librandi, Nov 12 2011

a(n) = ((n+3)*(2n+9)^n + 1)/(n+4).

cp's OEIS Frontend

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

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Maple

A083080 Main diagonal of number array A083075.

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Magma

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A083081 First superdiagonal of number array A083075.

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Magma

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A083083 A diagonal of number array A083075.

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Magma

Mathematica

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A083084 A diagonal of number array A083075.

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Magma

Formula

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