A293068 Sum of values of vertices of type D at level n of the hyperbolic Pascal pyramid PP_(4,5).

0, 0, 0, 6, 36, 170, 768, 3458, 15596, 70314, 316296, 1418538, 6342852, 28286258, 125865936, 559075586, 2479846748, 10987635738, 48642380568, 215198769114, 951576969588, 4206079161794, 18585710106720, 82106786841074, 362660527980812, 1601624618444970

Offset

0,4

Comments

Values divided by 2 are 0, 0, 0, 3, 18, 85, 384, 1729, 7798, 35157, 158148 ...

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 (4th line of Table 2).

Index entries for linear recurrences with constant coefficients, signature (12,-53,106,-94,28).

Formula

From Colin Barker, Oct 07 2017: (Start)

G.f.: 2*x^3*(3 - 18*x + 28*x^2) / ((1 - 2*x)*(1 - 4*x + 2*x^2)*(1 - 6*x + 7*x^2)).

a(n) = 12*a(n-1) - 53*a(n-2) + 106*a(n-3) - 94*a(n-4) + 28*a(n-5) for n>5.

(End)

Prog

(PARI) concat(vector(3), Vec(2*x^3*(3 - 18*x + 28*x^2) / ((1 - 2*x)*(1 - 4*x + 2*x^2)*(1 - 6*x + 7*x^2)) + O(x^30))) \\ Colin Barker, Oct 07 2017

Crossrefs

Cf. A293066, A293070.

Sequence in context: A203332 A351783 A190065 * A213294 A293886 A132165

Adjacent sequences: A293065 A293066 A293067 * A293069 A293070 A293071

Keyword

nonn,easy

Author

Eric M. Schmidt, Oct 03 2017

Status

approved