A292298 Sum of values of vertices of type D at level n of the hyperbolic Pascal pyramid.

0, 0, 0, 0, 24, 324, 3600, 38148, 398112, 4132596, 42818208, 443356212, 4589665248, 47509091508, 491769434400, 5090291998452, 52689326584800, 545383755284532, 5645229662006688, 58433377222329972, 604839778633231200, 6260653947359090868, 64803587809297981728

Offset: 0

Author

Eric M. Schmidt, Sep 14 2017

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..987
• László Németh, Hyperbolic Pascal pyramid, arXiv:1511.0267 [math.CO], 2015 (4th line of Table 2).
• Index entries for linear recurrences with constant coefficients, signature (18,-99,226,-224,92,-12).

Crossrefs

Cf. A264237.

Programs

Magma

I:=[0,0,0,0,24,324,3600]; [n le 7 select I[n] else 18*Self(n-1)-99*Self(n-2)+226*Self(n-3)-224*Self(n-4)+ 92*Self(n-5)-12*Self(n-6): n in [1..30]]; // Vincenzo Librandi, Sep 17 2017

Mathematica

Join[{0}, LinearRecurrence[{18, -99, 226, -224, 92, -12}, {0, 0, 0, 24, 324, 3600}, 20] ] (* Vincenzo Librandi, Sep 17 2017 *)
CoefficientList[Series[12*x^4*(2 - 9*x + 12*x^2)/((1 - x)*(1 - 4*x + 2*x^2)*(1 - 13*x + 28*x^2 - 6*x^3)), {x, 0, 20}], x] (* Wesley Ivan Hurt, Sep 17 2017 *)

PARI

concat(vector(4), Vec(12*x^4*(2 - 9*x + 12*x^2) / ((1 - x)*(1 - 4*x + 2*x^2)*(1 - 13*x + 28*x^2 - 6*x^3)) + O(x^30))) \\ Colin Barker, Sep 17 2017

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), n >= 7.

G.f.: 12*x^4*(2 - 9*x + 12*x^2) / ((1 - x)*(1 - 4*x + 2*x^2)*(1 - 13*x + 28*x^2 - 6*x^3)). - Colin Barker, Sep 17 2017