Trouble when computing A006743

[Robert G. Wilson v]

Dear Thomas,

	Using Mathematica: a[3] = 1; a[4] = 0; a[5] = 3; a[6] = 2; a[7] = 10; a[8] = 14; a[n_] := a[n] = ((2n - 6)a[n - 1] + (7n - 33)a[n - 2] + (-12n + 60)a[n - 3] + (-16n + 84)a[n - 4] + (16n - 96)a[n - 5] + (16n - 96)a[n - 6])/(n - 3); Table[a[n], {n, 3, 50}]

	I get: {1, 0, 3, 2, 10, 14, 40, 74, 177, 360, 809, 1694, 3709, 7824, 16895, 35650, 76282, 160638, 341372, 716930, 1515158, 3173066, 6675194, 13941234, 29213940, 60858542, 127101204, 264157338, 550071260, 1140775550, 2369405152, 4904222562, 10162968185, 20997881248, 43425513865, 89575908486, 184914605625, 380863356256, 784942478683, 1614512969690, 3322508791095, 6825333151504, 14026935003221, 28781782417814, 59077468341915, 121091211318372, 248271440541989, 508379512000178}

	So we agree that something is wrong with the recursive formula. I tried changing the offsets and several other coefficients but the results become fractions very quickly.

Sincerely, Bob.


Thomas Baruchel wrote:

> Hi, Simon Plouffe mentionned the A006743 sequence to me in a separate mail.
> I tried to compute it according to the formula, but I can't figure out
> what is wrong with my computation. Though I use Maxima syntax, you will
> understand very easely this piece of code even if you never used this
> software:
> 
> block([a6:1,a5:0,a4:3,a3:2,a2:10,a1:14],for n:9 thru 20 do block([a:(-6*
> a1+2*a1*n-33*a2+7*a2*n+60*a3-12*a3*n+84*a4-16*a4*n-96*a5+16*n*a5-96*a6+16*n*a6)/
> (n-3)],sprint(a,","),a6:a5,a5:a4,a4:a3,a3:a2,a2:a1,a1:a));
> 
> output being (for a_9, a_10, ...):
> 40 , 74 , 177 , 360 , 809 , 1694 , 3709 , 7824 , 16895 , 35650 , 76282 , 160638
> ,
> 
> instead of:
> 1,0,3,2,10,14,40,74,176,358,798,1670,3626,7638,16366,34462,
> 
>