A048923 -id:A048923 - cp's OEIS frontend

A048924 9-gonal octagonal numbers.

1, 631125, 286703855361, 130242107189808901, 59165603001256545014625, 26877395137662573622784125461, 12209701798707362366915379264832801, 5546550074879110936730454426529871893125

Offset: 1

Eric W. Weisstein

As n increases, this sequence is approximately geometric with common ratio r = lim_{n->infinity} a(n)/a(n-1) = (sqrt(6) + sqrt(7))^8 = 227137 + 35048*sqrt(42). - Ant King, Jan 03 2012

Vincenzo Librandi, Table of n, a(n) for n = 1..100
Eric Weisstein's World of Mathematics, Nonagonal Octagonal Number.
Index entries for linear recurrences with constant coefficients, signature (454275,-454275,1).

Cf. A048922, A048923.

I:=[1, 631125, 286703855361]; [n le 3 select I[n] else 454275*Self(n-1)-454275*Self(n-2)+Self(n-3): n in [1..10]]; // Vincenzo Librandi, Dec 24 2011

LinearRecurrence[{454275,-454275,1},{1,631125,286703855361},30] (* Vincenzo Librandi, Dec 24 2011 *)

a(n) = 454275*a(n-1) - 454275*a(n-2) + a(n-3). - Vincenzo Librandi, Dec 24 2011
From Ant King, Jan 03 2012: (Start)
G.f.: x*(1 + 176850*x + 261*x^2) / ((1-x)*(1 - 454274*x + x^2)).
a(n) = 454274*a(n-1) - a(n-2) + 177112.
a(n) = (1/672)*((11*sqrt(7) - 9*sqrt(6))*(sqrt(6) + sqrt(7))^(8*n-5) - (11*sqrt(7) + 9*sqrt(6))*(sqrt(6) - sqrt(7))^(8*n-5) - 262).
a(n) = floor((1/672)*(11*sqrt(7) - 9*sqrt(6))*(sqrt(6) + sqrt(7))^(8*n-5)). (End)

A048922 Indices of 9-gonal numbers which are also octagonal.

Original entry on oeis.org

1, 425, 286209, 192904201, 130017145025, 87631362842409, 59063408538638401, 39808649723679439625, 26830970850351403668609, 18084034544487122393202601, 12188612452013470141614884225

Offset: 1

Eric W. Weisstein

As n increases, this sequence is approximately geometric with common ratio r = lim_{n->infinity} a(n)/a(n-1) = (sqrt(6) + sqrt(7))^4 = 337 + 52*sqrt(42). - Ant King, Jan 03 2012

Vincenzo Librandi, Table of n, a(n) for n = 1..200
Eric Weisstein's World of Mathematics, Nonagonal Octagonal Numbers.
Index entries for linear recurrences with constant coefficients, signature (675,-675,1).

Cf. A048923, A048924.

I:=[1, 425, 286209]; [n le 3 select I[n] else 675*Self(n-1)-675*Self(n-2)+1*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Dec 23 2011

LinearRecurrence[{675,-675,1},{1,425,286209},30] (* Vincenzo Librandi, Dec 23 2011 *)
Join[{1},Transpose[NestList[{Last[#],674Last[#]-First[#]-240}&, {1,425}, 10]][[2]]] (* Harvey P. Dale, Feb 05 2012 *)

G.f.: -x*(1 - 250*x + 9*x^2) / ( (x-1)*(x^2 - 674*x + 1) ). - R. J. Mathar, Dec 21 2011
From Ant King, Jan 03 2012: (Start)
a(n) = 674*a(n-1) - a(n-2) - 240.
a(n) = (1/84)*((sqrt(6) + 3*sqrt(7))*(sqrt(6) + sqrt(7))^(4*n-3) + (sqrt(6) - 3*sqrt(7))*(sqrt(6) - sqrt(7))^(4*n-3) + 30).
a(n) = ceiling((1/84)*(sqrt(6) + 3*sqrt(7))*(sqrt(6) + sqrt(7))^(4*n-3)). (End)

cp's OEIS Frontend

A048924 9-gonal octagonal numbers.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

Formula