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 A064046 Number of length 6 walks on an n-dimensional hypercubic lattice starting and finishing at the origin and staying in the nonnegative part. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified March 4 15:24 EST 2024. Contains 370532 sequences. (Running on oeis4.)