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A227665 Number of lattice paths from {n}^3 to {0}^3 using steps that decrement one component by 1 such that for each point (p_1,p_2,p_3) we have abs(p_{i}-p_{i+1}) <= 1. 2
1, 6, 44, 320, 2328, 16936, 123208, 896328, 6520712, 47437640, 345104904, 2510609608, 18264477064, 132872558664, 966636864776, 7032203170760, 51158695924872, 372175277815624, 2707544336559112, 19697160911545032, 143295215053933448, 1042460827200624200 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (7,2).

FORMULA

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

a(n) = 7*a(n-1) + 2*a(n-2) for n>1, a(0)=1, a(2)=6.

EXAMPLE

a(1) = 3! = 3*2*1 = 6:

.         (0,1,1) - (0,0,1)

.       /         X         \

(1,1,1) - (1,0,1)   (0,1,0) - (0,0,0)

.       \         X         /

.         (1,1,0) - (1,0,0)

MAPLE

a:= n-> (<<0|1>, <2|7>>^n. <<1, 6>>)[1, 1]:

seq(a(n), n=0..25);

CROSSREFS

Column k=3 of A227655.

Cf. A000142.

Sequence in context: A156002 A091163 A189800 * A102591 A114935 A115969

Adjacent sequences:  A227662 A227663 A227664 * A227666 A227667 A227668

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Jul 19 2013

STATUS

approved

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Last modified August 9 22:52 EDT 2020. Contains 336335 sequences. (Running on oeis4.)