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

0,5

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).

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A264237.

Sequence in context: A006922 A036221 A022652 * A138453 A004317 A295250

Adjacent sequences: A292295 A292296 A292297 * A292299 A292300 A292301

Keyword

nonn,easy

Author

Eric M. Schmidt, Sep 14 2017

Status

approved