A293069 Sum of values of vertices of type E at level n of the hyperbolic Pascal pyramid PP_(4,5).

0, 0, 0, 0, 8, 70, 418, 2156, 10388, 48342, 220746, 996996, 4472564, 19975774, 88948426, 395220140, 1753302020, 7768999014, 34394485578, 152166756084, 672863006900, 2974140030862, 13142067477610, 58058237351324, 256439661695684, 1132519514646870

Offset

0,5

Comments

Values divided by 2 are 0, 0, 0, 0, 4, 35, 209, 1078, 5194, 24171, 110373, ...

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 (5th line of Table 2).

Index entries for linear recurrences with constant coefficients, signature (13,-65,159,-200,122,-28).

Formula

a(n) = 13*a(n-1) - 65*a(n-2) + 159*a(n-3) - 200*a(n-4) + 122*a(n-5) - 28*a(n-6), n >= 7.

G.f.: 2*x^4*(4 - 17*x + 14*x^2) / ((1 - x)*(1 - 2*x)*(1 - 4*x + 2*x^2)*(1 - 6*x + 7*x^2)). - Colin Barker, Oct 07 2017

Mathematica

LinearRecurrence[{13, -65, 159, -200, 122, -28}, {0, 0, 0, 0, 8, 70, 418}, 30] (* Harvey P. Dale, Oct 29 2023 *)

Prog

(PARI) concat(vector(4), Vec(2*x^4*(4 - 17*x + 14*x^2) / ((1 - x)*(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: A376855 A209074 A124152 * A056631 A190560 A266361

Adjacent sequences: A293066 A293067 A293068 * A293070 A293071 A293072

Keyword

nonn,easy

Author

Eric M. Schmidt, Oct 03 2017

Status

approved