A288352 -id:A288352 - cp's OEIS frontend

A288351 Number of strings of n digits from 1...9 such that no formula using the single digits in the given order exists that evaluates to 0.

9, 72, 455, 1500, 1014, 181, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Hugo Pfoertner, Jun 08 2017

nonn

For definitions and comments see A288350.
It is conjectured that a(n)=0 for n>=8.
The conjecture is true, as shown in the corresponding comment in A288350. - Hugo Pfoertner, Jun 09 2017

			a(1)=9 because 1...9 /=0. a(2)=72, because only the 9 numbers 11, 22, ..., 99 of the 81 two-digit strings can represent 0.

Cf. A288350, A288352, A288353, A288354, A288355, A288356.

A288550 Number of strings of n digits from 1...9 such that a signed summation of the digits exists making the sum = 0.

Original entry on oeis.org

1, 0, 9, 108, 1569, 20230, 229203, 2278745, 21214753, 192899244, 1741242069, 15684465423, 141196229849, 1270871708340, 11438182427193, 102944790695746, 926507214592705, 8338579980466304, 75047276148618205, 675425698975426255, 6078832109331582297

Offset: 0

Hugo Pfoertner, Jun 11 2017

			a(2)=9, because 11, 22, ..., 99 can be written as 1-1=0, 2-2=0, ...

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).

Cf. A065024, A065025, A065086, A288351, A288352.

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

a(11)-a(20) from Alois P. Heinz, Jun 11 2017

A288502 Strings of digits from 1...9 such that any possible formula using the single digits in the given order that evaluates to 0 needs to include at least one division.

Original entry on oeis.org

263, 284, 362, 393, 482, 1262, 1284, 1293, 1382, 1393, 1482, 1493, 1631, 1823, 1841, 1932, 1934, 2162, 2173, 2184, 2193, 2194, 2195, 2346, 2375, 2593, 2597, 2612, 2621, 2625, 2638, 2658, 2674, 2713, 2735, 2813, 2814, 2831, 2841, 2843, 2845, 2847, 2849, 2859, 2895, 2914

Offset: 1

Hugo Pfoertner, Jun 10 2017

For definitions see A288350.

			1262 is in the sequence, because no formula with result 0 avoiding divisions can be found, but 0=1+2-(6/2). A file with examples of formulas for all sequence terms is provided, see link section.

Hugo Pfoertner, Table of n, a(n) for n = 1..1009
Hugo Pfoertner, Formulas with result 0 for all sequence terms.

Cf. A288350, A288352.

cp's OEIS Frontend

A288351 Number of strings of n digits from 1...9 such that no formula using the single digits in the given order exists that evaluates to 0.

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A288550 Number of strings of n digits from 1...9 such that a signed summation of the digits exists making the sum = 0.

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A288502 Strings of digits from 1...9 such that any possible formula using the single digits in the given order that evaluates to 0 needs to include at least one division.

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Author

Keywords

Comments

Examples

Links

Crossrefs