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A293067 Sum of values of vertices of type A at level n of the hyperbolic Pascal pyramid PP_(4,5). 1
0, 0, 2, 6, 18, 58, 194, 658, 2242, 7650, 26114, 89154, 304386, 1039234, 3548162, 12114178, 41360386, 141213186, 482131970, 1646101506, 5620142082, 19188365314, 65513177090, 223675977730, 763677556738, 2607358271490, 8902077972482, 30393595346946 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Values divided by 2 are 0, 0, 1, 3, 9, 29, 97, 329, 1121, 3825, 13057, ...

LINKS

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

László Németh, Pascal pyramid in the space H^2 x R, arXiv:1701.06022 [math.CO], 2017 (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 >= 3.

From Colin Barker, Oct 07 2017: (Start)

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

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

(End)

MATHEMATICA

LinearRecurrence[{5, -6, 2}, {0, 0, 2, 6}, 30] (* Harvey P. Dale, May 24 2019 *)

PROG

(PARI) concat(vector(2), Vec(2*x^2*(1 - 2*x) / ((1 - x)*(1 - 4*x + 2*x^2)) + O(x^30))) \\ Colin Barker, Oct 07 2017

CROSSREFS

Cf. A293066, A293070.

Sequence in context: A151282 A193777 A157004 * A085139 A150041 A190790

Adjacent sequences:  A293064 A293065 A293066 * A293068 A293069 A293070

KEYWORD

nonn,easy

AUTHOR

Eric M. Schmidt, Sep 30 2017

STATUS

approved

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Last modified July 12 18:03 EDT 2020. Contains 335666 sequences. (Running on oeis4.)