Michael Tulskikh - cp's OEIS frontend

A336630 a(n) = 2F(2n+1) + 4F(n+1)F(n-1) for n > 0, with a(0) = 0 and F(n) = A000045(n).

0, 4, 18, 38, 108, 274, 726, 1892, 4962, 12982, 33996, 88994, 232998, 609988, 1596978, 4180934, 10945836, 28656562, 75023862, 196415012, 514221186, 1346248534, 3524524428, 9227324738, 24157449798, 63245024644, 165577624146, 433487847782

Offset: 0

Michael Tulskikh, Jul 28 2020

Index entries for linear recurrences with constant coefficients, signature (2,2,-1).

Cf. A000045, A001519, A059929.

a(n) = (F(4n+1) - F(n+1)^4)/F(n)^2 for n > 0 and a(0) = 0, where F(n) = A000045(n).
a(n) = 2*A001519(n+1) + 4*A059929(n-1) for n > 0.
From Stefano Spezia, Jul 28 2020: (Start)
O.g.f.: 2*x*(2 + 5*x - 3*x^2)/(1 - 2*x - 2*x^2 + x^3).
a(n) = 2*a(n-1) + 2*a(n-2) - a(n-2) for n > 3. (End)

A335274 a(n) = 2*a(n-1) + a(n-3), where a(0) = 0, a(1) = 1, a(2) = 4.

Original entry on oeis.org

0, 1, 4, 8, 17, 38, 84, 185, 408, 900, 1985, 4378, 9656, 21297, 46972, 103600, 228497, 503966, 1111532, 2451561, 5407088, 11925708, 26302977, 58013042, 127951792, 282206561, 622426164, 1372804120, 3027814801, 6678055766, 14728915652, 32485646105, 71649347976

Offset: 0

Michael Tulskikh, May 30 2020

a(n) is the number of ways to tile a 2 x n strip, with a bent tromino added to the top, with dominos and L-shaped trominos:
   _
  ||
  |||_  
  |||_||| . . .
  |||_||| . . .

			a(2) = 4 as shown by these four tilings:
   _         _         _         _
  |X|_      | |_      |X|_      | |_
  |X|X|  ,  |_|X|  ,  |X|X|  ,  |_| |
  |_ _|     |X X|     | | |     |X|_|
  |_ _|     |_ _|     |_|_|     |X X|

Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,0,1).

Cf. A008998, A335242.

LinearRecurrence[{2, 0, 1}, {0, 1, 4}, 50] (* Paolo Xausa, Mar 20 2025 *)

concat(0, Vec(x*(1 + 2*x) / (1 - 2*x - x^3) + O(x^35))) \\ Colin Barker, Jun 04 2020

a(n) = 2*a(n-1) + a(n-3).
a(n) = 2*A008998(n-1) - A008998(n-4).
a(n) = A008998(n-1) + 2*A008998(n-2).
G.f.: x*(1 + 2*x) / (1 - 2*x - x^3). - Colin Barker, Jun 04 2020

A332491 a(n) = 2*a(n-1) + a(n-3), where a(0) = 3, a(1) = 1, a(2) = 2.

Original entry on oeis.org

3, 1, 2, 7, 15, 32, 71, 157, 346, 763, 1683, 3712, 8187, 18057, 39826, 87839, 193735, 427296, 942431, 2078597, 4584490, 10111411, 22301419, 49187328, 108486067, 239273553, 527734434, 1163954935, 2567183423, 5662101280, 12488157495, 27543498413

Offset: 0

Michael Tulskikh, Feb 13 2020

Index entries for linear recurrences with constant coefficients, signature (2,0,1).

LinearRecurrence[{2,0,1},{3,1,2},40] (* Harvey P. Dale, Apr 20 2025 *)

a(n) = 2*a(n-1) + a(n-3).
a(n) = A052980(n) + 2*A008998(n-3).
a(n) = A008998(n-1) + 3*A008998(n-3).
G.f.: (5x-3)/(x^3+2*x-1).

cp's OEIS Frontend

User: Michael Tulskikh

A336630 a(n) = 2F(2n+1) + 4F(n+1)F(n-1) for n > 0, with a(0) = 0 and F(n) = A000045(n).

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A335274 a(n) = 2*a(n-1) + a(n-3), where a(0) = 0, a(1) = 1, a(2) = 4.

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A332491 a(n) = 2*a(n-1) + a(n-3), where a(0) = 3, a(1) = 1, a(2) = 2.

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cp's OEIS Frontend

User: Michael Tulskikh

A336630 a(n) = 2*F(2*n+1) + 4*F(n+1)*F(n-1) for n > 0, with a(0) = 0 and F(n) = A000045(n).

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Author

Keywords

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Crossrefs

Formula

A335274 a(n) = 2*a(n-1) + a(n-3), where a(0) = 0, a(1) = 1, a(2) = 4.

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Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A332491 a(n) = 2*a(n-1) + a(n-3), where a(0) = 3, a(1) = 1, a(2) = 2.

Views

Author

Keywords

Links

Programs

Mathematica

Formula

A336630 a(n) = 2F(2n+1) + 4F(n+1)F(n-1) for n > 0, with a(0) = 0 and F(n) = A000045(n).