A393661 A sequence appearing in the 3-Bratteli diagram, a(n)=3^(n-3)*(16*n-17), n>=3.

31, 141, 567, 2133, 7695, 26973, 92583, 312741, 1043199, 3444525, 11278359, 36669429, 118511343, 381043197, 1219657095, 3888553797, 12354408927, 39129469389, 123587135991, 389357591445, 1223861324751, 3838949625501, 12018945830247, 37563128351973, 117208257639615, 365181390669933

Offset

3,1

Comments

a(n) denotes the total number of descents of all paths starting from a vertex on the 2(n+1)-th floor in the 3-Bratteli diagram and ending at all vertices on the first floor.

Links

Tamilselvi Annamalai, Table of n, a(n) for n = 3..102

Wikipedia, Bratteli diagram.

Index entries for linear recurrences with constant coefficients, signature (6,-9).

Formula

a(n) = 3^(n-3)*(16*n-17).

G.f.: x^3*(31-45*x)/(1-3*x)^2.

E.g.f.: (34 + 6*x - 135*x^2 + exp(3*x)*(96*x - 34))/54. - Stefano Spezia, Feb 25 2026

Maple

a(n):= 3^(n - 3)*(16*n - 17);
num_list := [seq(eval(a(n), n = i), i = 3 .. 100)];

Mathematica

LinearRecurrence[{6, -9}, {31, 141}, 26] (* Hugo Pfoertner, Feb 24 2026 *)

Crossrefs

Cf. A391520, A393655, A393662.

Sequence in context: A201960 A182916 A233303 * A185521 A228261 A185513

Adjacent sequences: A393658 A393659 A393660 * A393662 A393663 A393664

Keyword

nonn,easy

Author

Tamilselvi Annamalai, Feb 24 2026

Status

approved