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A064043 Number of length 3 walks on an n-dimensional hypercubic lattice starting at the origin and staying in the nonnegative part. 5
0, 3, 18, 51, 108, 195, 318, 483, 696, 963, 1290, 1683, 2148, 2691, 3318, 4035, 4848, 5763, 6786, 7923, 9180, 10563, 12078, 13731, 15528, 17475, 19578, 21843, 24276, 26883, 29670, 32643, 35808, 39171, 42738, 46515, 50508, 54723, 59166, 63843 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..1000

D. R. L. Brown, Bounds on surmising remixed keys, IACR, Report 2015/375, 2015-2016. See Table 1.

FORMULA

a(n) = n*(n^2 + 3n -1) = n*A014209(n) = A064044(n, 3).

a(n) = a(n-1) + 3*A002378(n-1) + 6*A001477(n-1) + 3*A000012(n-1).

G.f.: 3*x*(1+2*x-x^2)/(1-x)^4. - Colin Barker, Apr 19 2012

E.g.f.: (x^3 + 6*x^2 + 3*x)*exp(x). - G. C. Greubel, Jul 20 2017

a(n) = A084990(n)/3. - Alois P. Heinz, Jul 21 2017

MAPLE

seq(sum(3*n+n^2-1, k=1..n), n=0..39); # Zerinvary Lajos, Jan 28 2008

MATHEMATICA

Table[n*(n^2 + 3n -1), {n, 0, 50}] (* G. C. Greubel, Jul 20 2017 *)

PROG

(PARI) { for (n=0, 1000, write("b064043.txt", n, " ", n*(n^2 + 3*n - 1)) ) } \\ Harry J. Smith, Sep 06 2009

CROSSREFS

Number of walks length 0, 1 and 2 are A000012, A001477 and A002378.

Cf. A084990.

Sequence in context: A138976 A275038 A304976 * A267639 A238649 A268484

Adjacent sequences:  A064040 A064041 A064042 * A064044 A064045 A064046

KEYWORD

nonn,easy

AUTHOR

Henry Bottomley, Aug 23 2001

STATUS

approved

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Last modified July 4 14:51 EDT 2020. Contains 335448 sequences. (Running on oeis4.)