A064043 - OEIS

%I #30 Feb 10 2018 09:51:27

%S 0,3,18,51,108,195,318,483,696,963,1290,1683,2148,2691,3318,4035,4848,

%T 5763,6786,7923,9180,10563,12078,13731,15528,17475,19578,21843,24276,

%U 26883,29670,32643,35808,39171,42738,46515,50508,54723,59166,63843

%N Number of length 3 walks on an n-dimensional hypercubic lattice starting at the origin and staying in the nonnegative part.

%H Harry J. Smith, <a href="/A064043/b064043.txt">Table of n, a(n) for n = 0..1000</a>

%H D. R. L. Brown, <a href="https://ia.cr/2015/375">Bounds on surmising remixed keys</a>, IACR, Report 2015/375, 2015-2016. See Table 1.

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

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

%F G.f.: 3*x*(1+2*x-x^2)/(1-x)^4. - _Colin Barker_, Apr 19 2012

%F E.g.f.: (x^3 + 6*x^2 + 3*x)*exp(x). - _G. C. Greubel_, Jul 20 2017

%F a(n) = A084990(n)/3. - _Alois P. Heinz_, Jul 21 2017

%p seq(sum(3*n+n^2-1, k=1..n), n=0..39); # _Zerinvary Lajos_, Jan 28 2008

%t Table[n*(n^2 + 3n -1), {n,0,50}] (* _G. C. Greubel_, Jul 20 2017 *)

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

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

%Y Cf. A084990.

%K nonn,easy

%O 0,2

%A _Henry Bottomley_, Aug 23 2001