A293070 Sum of values of vertices at level n of the hyperbolic Pascal pyramid PP_(4,5).

1, 3, 9, 29, 103, 399, 1641, 6989, 30319, 132735, 583665, 2571821, 11343223, 50052495, 220904217, 975041453, 4303886431, 18997962879, 83860441185, 370176644813, 1634036256295, 7212979975503, 31839623961801, 140546879747981, 620403902366671, 2738595239186943

Offset

0,2

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 (6th line of Table 2).

Index entries for linear recurrences with constant coefficients, signature (8,-19,14).

Formula

a(n) = 8*a(n-1) - 19*a(n-2) + 14*a(n-3), n >= 3.

From Colin Barker, Oct 07 2017: (Start)

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

a(n) = (2^(2+n) - (3-sqrt(2))^n*(1+sqrt(2)) + (-1+sqrt(2))*(3+sqrt(2))^n) / 2.

(End)

Prog

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

Crossrefs

Cf. A293066.

Sequence in context: A109432 A148943 A148944 * A060719 A091152 A148945

Adjacent sequences: A293067 A293068 A293069 * A293071 A293072 A293073

Keyword

nonn,easy

Author

Eric M. Schmidt, Oct 03 2017

Status

approved