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A371596
The number of unilevel points (unique points at their height) on Delannoy paths ending when x = n.
1
1, 4, 8, 20, 48, 116, 280, 676, 1632, 3940, 9512, 22964, 55440, 133844, 323128, 780100, 1883328, 4546756, 10976840, 26500436, 63977712, 154455860, 372889432, 900234724, 2173358880, 5246952484, 12667263848, 30581480180, 73830224208, 178241928596, 430314081400
OFFSET
0,2
FORMULA
G.f.: (1 + 2*x - x^2)/(1 - 2*x - x^2).
a(n) = 4 * A000129(n) for n >= 1.
EXAMPLE
There are 5 paths ending with x=2. Of these, UU has 3 unilevel points, UD has 1, L has none, DU has 1, and DD has 3.
MATHEMATICA
CoefficientList[Series[(1+2*x-x^2)/(1-2*x-x^2), {x, 0, 24}], x]
CROSSREFS
Sequence in context: A203167 A123861 A357287 * A115099 A060919 A009333
KEYWORD
nonn,easy
AUTHOR
Lou Shapiro, Mar 28 2024
STATUS
approved