login
A293069
Sum of values of vertices of type E at level n of the hyperbolic Pascal pyramid PP_(4,5).
1
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
László Németh, Pascal pyramid in the space H^2 x R, arXiv:1701.06022 [math.CO], 2017 (5th line of Table 2).
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
Sequence in context: A376855 A209074 A124152 * A056631 A190560 A266361
KEYWORD
nonn,easy
AUTHOR
Eric M. Schmidt, Oct 03 2017
STATUS
approved