A083078 -id:A083078 - 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

A083077 Fifth row of number array A083075.

Original entry on oeis.org

1, 9, 97, 1065, 11713, 128841, 1417249, 15589737, 171487105, 1886358153, 20749939681, 228249336489, 2510742701377, 27618169715145, 303799866866593, 3341798535532521, 36759783890857729, 404357622799435017

Offset: 0

Paul Barry, Apr 23 2003

Vincenzo Librandi, Table of n, a(n) for n = 0..900
Index entries for linear recurrences with constant coefficients, signature (12,-11).

Cf. A083076, A066443, A083078.

[(4*11^n+1)/5: n in [0..30]]; // Vincenzo Librandi, Nov 10 2011

LinearRecurrence[{12,-11},{1,9},30] (* Harvey P. Dale, Jun 14 2015 *)

a(n) = (4*11^n + 1)/5.
G.f.: (1-3*x)/((1-x)*(1-11*x)).
E.g.f.: (4*exp(11*x) + exp(x))/5.
a(n) = 11*a(n-1) - 2, a(n) = 12*a(n-1) - 11*a(n-2). - Vincenzo Librandi, Nov 10 2011

cp's OEIS Frontend

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

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A083077 Fifth row of number array A083075.

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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

A083077 Fifth row of number array A083075.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

Formula

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