A097076 -id:A097076 - cp's OEIS frontend

A166867 a(n) = Pell(n+3) - Jacobsthal(n+4).

0, 1, 8, 27, 84, 237, 644, 1695, 4376, 11129, 28000, 69859, 173180, 427141, 1049308, 2569447, 6275584, 15295377, 37215864, 90426155, 219466276, 532154909, 1289368500, 3122076719, 7555891560, 18278599081, 44202568208, 106862692467

Offset: 0

Paul Barry, Oct 22 2009

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,1,-5,-2).

Cf. A000129, A097076, A166868.

LinearRecurrence[{3, 1, -5, -2}, {0, 1, 8, 27}, 50] (* G. C. Greubel, May 25 2016 *)

G.f.: x(1+5x+2x^2)/((1-x-2x^2)(1-2x-x^2)).
a(n) = A166868(n) + A097076(n+1) - A000129(n+2).
a(n) = 3*a(n-1) + a(n-2) - 5*a(n-3) - 2*a(n-4). - G. C. Greubel, May 25 2016

A358715 a(n) is the number of distinct ways to cut an equilateral triangle with edges of size n into equilateral triangles with integer sides.

Original entry on oeis.org

1, 2, 5, 26, 220, 3622, 105859, 5677789, 553715341, 98404068313, 31850967186980, 18779046566454536, 20167518569123722322, 39451359692134386945019

Offset: 1

Craig Knecht and John Mason, Nov 28 2022

In other words, the number of equilateral triangular tilings of an equilateral triangle, where rotations and reflections are considered distinct.

			a(3)=5 because of:
    /\      /\      /\      /\      /\
   /  \    /\/\    /  \    /\/\    /\/\
  /    \  /  \/\  /\/\/\  /\/  \  /\/\/\

Cf. A045846, A097076, A358716.

Cf. A290820, A290821, A299705, A300001.

a(10)-a(14) from Walter Trump, Dec 03 2022

A137199 a(n)=a(n-1)+3a(n-2)+a(n-3).

Original entry on oeis.org

1, 1, 1, 5, 9, 25, 57, 141, 337, 817, 1969, 4757, 11481, 27721, 66921, 161565, 390049, 941665, 2273377, 5488421, 13250217, 31988857, 77227929, 186444717, 450117361, 1086679441, 2623476241, 6333631925, 15290740089, 36915112105, 89120964297

Offset: 0

Paul Curtz, Mar 04 2008

Index entries for linear recurrences with constant coefficients, signature (1,3,1)

Cf. A097076.

LinearRecurrence[{1,3,1},{1,1,1},40] (* Harvey P. Dale, Feb 27 2020 *)

O.g.f.: (-1+3*x^2)/{(1+x)(x^2+2*x-1)} . a(n) = (-1)^(n+1)+2*A000129(n-1) if n>=1. - R. J. Mathar, Mar 17 2008

cp's OEIS Frontend

A166867 a(n) = Pell(n+3) - Jacobsthal(n+4).

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A358715 a(n) is the number of distinct ways to cut an equilateral triangle with edges of size n into equilateral triangles with integer sides.

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A137199 a(n)=a(n-1)+3a(n-2)+a(n-3).

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