A288550 Number of strings of n digits from 1...9 such that a signed summation of the digits exists making the sum = 0.
1, 0, 9, 108, 1569, 20230, 229203, 2278745, 21214753, 192899244, 1741242069, 15684465423, 141196229849, 1270871708340, 11438182427193, 102944790695746, 926507214592705, 8338579980466304, 75047276148618205, 675425698975426255, 6078832109331582297
Offset: 0
Examples
a(2)=9, because 11, 22, ..., 99 can be written as 1-1=0, 2-2=0, ...
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..1048
- Index entries for linear recurrences with constant coefficients, signature (26, -267, 1374, -3360, 528, 17604, -35208, -9102, 110796, -90426, -134652, 238980, 28056, -272460, 102552, 155751, -117462, -34643, 53134, -4668, -9144, 2592).
Formula
Limit_{n->oo} a(n)/9^n = 1/2.
G.f.: (4447872*x^35 +731808*x^34 -31561200*x^33 -9438744*x^32 +95630316*x^31 +43022340*x^30 -156898794*x^29 -98774388*x^28 +140941738*x^27 +120112934*x^26 -46571519*x^25 -49352408*x^24 -50794519*x^23 -70733352*x^22 +118351595*x^21 +120154070*x^20 -162641593*x^19 -54549200*x^18 +156403902*x^17 -38131997*x^16 -93427552*x^15 +56672934*x^14 +28535743*x^13 -26850890*x^12 -1996107*x^11 +5000082*x^10 -264871*x^9 -434046*x^8 +41593*x^7 +13610*x^6 +4622*x^5 -4524*x^4 +1500*x^3 -276*x^2 +26*x -1) / ((9*x-1) *(4*x-1) *(3*x-1)^2 *(2*x-1)^3 *(x+1)^7 *(x-1)^8). - Alois P. Heinz, Jun 11 2017
a(n) = (9^n - A065025(n))/2 for n>0. - Alois P. Heinz, Jun 12 2017
Extensions
a(11)-a(20) from Alois P. Heinz, Jun 11 2017