A292295 Sum of values of vertices of type A at level n of the hyperbolic Pascal pyramid.

0, 0, 6, 18, 54, 174, 582, 1974, 6726, 22950, 78342, 267462, 913158, 3117702, 10644486, 36342534, 124081158, 423639558, 1446395910, 4938304518, 16860426246, 57565095942, 196539531270, 671027933190, 2291032670214, 7822074814470, 26706233917446, 91180786040838

Offset

0,3

Links

Colin Barker, Table of n, a(n) for n = 0..1000

László Németh, Hyperbolic Pascal pyramid, arXiv:1511.0267 [math.CO], 2015 (1st line of Table 2).

Index entries for linear recurrences with constant coefficients, signature (5,-6,2).

Formula

a(n) = 5*a(n-1) - 6*a(n-2) + 2*a(n-3), n >= 4.

From Colin Barker, Sep 17 2017: (Start)

G.f.: 6*x^2*(1 - 2*x) / ((1 - x)*(1 - 4*x + 2*x^2)).

a(n) = (-3/2)*(-4 + (4-3*sqrt(2))*(2+sqrt(2))^n + (2-sqrt(2))^n*(4+3*sqrt(2))) for n>0.

(End)

Mathematica

CoefficientList[Series[6*x^2*(1 - 2*x)/((1 - x)*(1 - 4*x + 2*x^2)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Sep 17 2017 *)

Prog

(PARI) concat(vector(2), Vec(6*x^2*(1 - 2*x) / ((1 - x)*(1 - 4*x + 2*x^2)) + O(x^30))) \\ Colin Barker, Sep 17 2017

Crossrefs

Cf. A264237.

Sequence in context: A002933 A016089 A099856 * A183913 A056349 A278768

Adjacent sequences: A292292 A292293 A292294 * A292296 A292297 A292298

Keyword

nonn,easy

Author

Eric M. Schmidt, Sep 13 2017

Status

approved