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A292295 Sum of values of vertices of type A at level n of the hyperbolic Pascal pyramid. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
László Németh, Hyperbolic Pascal pyramid, arXiv:1511.0267 [math.CO], 2015 (1st line of Table 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
KEYWORD
nonn,easy
AUTHOR
Eric M. Schmidt, Sep 13 2017
STATUS
approved

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Last modified June 13 17:15 EDT 2024. Contains 373391 sequences. (Running on oeis4.)