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A264236 Number of vertices at level n of the hyperbolic Pascal pyramid. 7
1, 3, 6, 13, 36, 138, 736, 4908, 36351, 280228, 2190651, 17206203, 135357481, 1065387963, 8387050686, 66029196613, 519841755036, 4092692363058, 32221664474776, 253680537891828, 1997222414704551, 15724098193422028, 123795561597659331, 974640390569138163 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

László Németh, Hyperbolic Pascal pyramid, arXiv:1511.02067 [math.CO], 2015 (6th line of Table 1).

Index entries for linear recurrences with constant coefficients, signature (12,-37,37,-12,1).

FORMULA

a(n) = 12*a(n-1) - 37*a(n-2) + 37*a(n-3) - 12*a(n-4) + a(n-5).

a(n) = (-3/2 + 9*sqrt(5)/10)*((3 + sqrt(5))/2)^n + (-3/2 - 9*sqrt(5)/10)*((3 - sqrt(5))/2)^n + (7/12 - 3*sqrt(15)/20)*(4 + sqrt(15))^n + (7/12 + 3*sqrt(15)/20)*(4 - sqrt(15))^n + 17/6. (See Németh paper, page 9.)

G.f.: (1 - 9*x + 7*x^2 + 15*x^3 + 3*x^4)/((1 - x)*(1 - 3*x + x^2)*(1 - 8*x + x^2)). [Bruno Berselli, Nov 09 2015]

MATHEMATICA

LinearRecurrence[{12, -37, 37, -12, 1}, {1, 3, 6, 13, 36}, 30] (* Bruno Berselli, Nov 09 2015 *)

PROG

(PARI) Vec((1-9*x+7*x^2+15*x^3+3*x^4)/((1-x)*(1-3*x+x^2)*(1-8*x+x^2)) + O(x^50)) \\ Altug Alkan, Nov 09 2015

CROSSREFS

Cf. A027941, A055588, A264237.

Sequence in context: A104448 A062466 A053564 * A216999 A036781 A084816

Adjacent sequences:  A264233 A264234 A264235 * A264237 A264238 A264239

KEYWORD

nonn,easy

AUTHOR

Michel Marcus, Nov 09 2015

EXTENSIONS

More terms from Bruno Berselli, Nov 09 2015

STATUS

approved

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Last modified September 22 20:30 EDT 2018. Contains 315270 sequences. (Running on oeis4.)