A264237 Sum of values of vertices at level n of the hyperbolic Pascal pyramid.

1, 3, 9, 33, 165, 1137, 9837, 95193, 962541, 9884889, 102049197, 1055383929, 10921055661, 113032307769, 1169952636525, 12109971475065, 125349031354029, 1297477519769145, 13430093334225645, 139013932289379321, 1438923355509080877, 14894194022848480185

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..987

László Németh, Hyperbolic Pascal pyramid, arXiv:1511.02067 [math.CO], 2015 (6th line of Table 2).

Index entries for linear recurrences with constant coefficients, signature (18,-99,226,-224,92,-12).

Formula

a(n) = 18*a(n-1) - 99*a(n-2) + 226*a(n-3) - 224*a(n-4) + 92*a(n-5) - 12*a(n-6), for n >= 7.

G.f.: -(20*x^5-8*x^4+58*x^3-54*x^2+15*x-1) / ((x-1)*(2*x^2-4*x+1)*(6*x^3-28*x^2+13*x-1)). - Colin Barker, Nov 09 2015

Mathematica

CoefficientList[Series[-(20*x^5 - 8*x^4 + 58*x^3 - 54*x^2 + 15*x - 1)/((x - 1)*(2*x^2 - 4*x + 1)*(6*x^3 - 28*x^2 + 13*x - 1)), {x, 0, 20}], x] (* Wesley Ivan Hurt, Sep 17 2017 *)

Prog

(PARI) Vec(-(20*x^5-8*x^4+58*x^3-54*x^2+15*x-1)/((x-1)*(2*x^2-4*x+1)*(6*x^3-28*x^2+13*x-1)) + O(x^30)) \\ Colin Barker, Nov 09 2015

Crossrefs

Cf. A035344, A264236.

Sequence in context: A007489 A294638 A201968 * A097677 A138769 A100076

Adjacent sequences: A264234 A264235 A264236 * A264238 A264239 A264240

Keyword

nonn,easy

Author

Michel Marcus, Nov 09 2015

Extensions

Definition edited by Eric M. Schmidt, Sep 17 2017

Status

approved