seq: Number of self-avoiding walks on cubic lattice with no more than n steps
Joerg Arndt
arndt at jjj.de
Sun Jun 29 03:24:31 CEST 2008
I find the sequence definitely worth submitting.
* Jonathan Post <jvospost3 at gmail.com> [Jun 29. 2008 10:39]:
> Number of self-avoiding walks on cubic lattice with no more than n steps.
>
> 1, 7, 37, 187, 913, 4447, 21373, 102763, 490729, 2344615, 11154493,
> 53088643, 251931385, 1195905895, 5664817573, 26839963627,
> 126961839601, 600692091703, 2838415775797, 13414448995411,
> 63331776834145, 299041867336303, 1410823850778709, 6656812065970123
>
> Formula
> Partial sum of A001412
>
> Offset
> 0,2
>
> Example:
> a(9) = 1 + 6 + 30 + 150 + 726 + 3534 + 16926 + 81390 + 387966 +
> 1853886 = 2344615
>
> Comment:
> Primes include a(1) = 7, a(2) = 37, a(5) = 4447, a(8) = 102763, a(15)
> = 26839963627.
>
> Cf. A001412, A002902, A078717, A001411, A001413.
>
> Keywords:
> nonn,walk
>
> Not all partial sums are desired, but this one seems natural and
> non-arbitrary to me. Anyone find this worth submitting?
>
> Best,
>
> Jonathan Vos Post
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