A064046 Number of length 6 walks on an n-dimensional hypercubic lattice starting and finishing at the origin and staying in the nonnegative part.

0, 5, 70, 285, 740, 1525, 2730, 4445, 6760, 9765, 13550, 18205, 23820, 30485, 38290, 47325, 57680, 69445, 82710, 97565, 114100, 132405, 152570, 174685, 198840, 225125, 253630, 284445, 317660, 353365, 391650, 432605, 476320, 522885, 572390

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n) = 5*n*(3*n^2 - 3*n + 1).

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).

a(n) = A064045(n, 3).

a(n) = a(n-1) + 15*A049450(n-1) + 30*A001477(n-1) + 5*A000012(n-1).

G.f.: 5*x*(7*x^2 + 10*x + 1)/(x-1)^4. [Colin Barker, Jul 21 2012]

Mathematica

LinearRecurrence[{4, -6, 4, -1}, {0, 5, 70, 285}, 40] (* Harvey P. Dale, Dec 02 2012 *)

Prog

(Magma) [5*n*(3*n^2-3*n+1): n in [0..40]]; // Vincenzo Librandi, Jun 16 2011

Crossrefs

Numbers of walks of length 0, 1, 2, 3, 4 and 5 are A000012, A000004, A001477, A000004, A049450 and A000004.

Sequence in context: A218709 A286840 A034944 * A256235 A142588 A246154

Adjacent sequences: A064043 A064044 A064045 * A064047 A064048 A064049

Keyword

nonn,easy

Author

Henry Bottomley, Aug 23 2001

Status

approved