A271894 Expansion of (1+x-3*x^2) / ( 1-2*x-4*x^2+6*x^3 ).

1, 3, 7, 20, 50, 138, 356, 964, 2524, 6768, 17848, 47624, 126032, 335472, 889328, 2364352, 6273184, 16667808, 44242240, 117516608, 311995328, 828603648, 2200088960, 5842620544, 15513975040, 41197898496, 109395973888, 290499691520, 771395887616

Offset: 0

Author

R. J. Mathar, Apr 16 2016

Keywords

• nonn
• easy

Comments

Sum of all second elements at level n of the TRIP-Stern sequence corresponding to the permutation triple (e,13,23)

Links

• Ilya Amburg, Krishna Dasaratha, Laure Flapan, Thomas Garrity, Chansoo Lee, Cornelia Mihaila, Nicholas Neumann-Chun, Sarah Peluse, Matthew Stoffregen, Stern Sequences for a Family of Multidimensional Continued Fractions: TRIP-Stern Sequences, arXiv:1509.05239 [math.CO], 2015, Section 7.2.1
• Index entries for linear recurrences with constant coefficients, signature (2,4,-6).

Crossrefs

Cf. A271486 (maximum at level n).

Programs

Mathematica

CoefficientList[Series[(1+x-3x^2)/(1-2x-4x^2+6x^3),{x,0,30}],x] (* or *) LinearRecurrence[{2,4,-6},{1,3,7},30] (* Harvey P. Dale, Jul 14 2024 *)

PARI

x='x+O('x^99); Vec((1+x-3*x^2)/(1-2*x-4*x^2+6*x^3)) \\ Altug Alkan, Apr 16 2016

Formula

a(n) >= 2^n.