A333405 Number of integers in base n having exactly three distinct digits such that the number formed by the consecutive subsequence of the initial j digits is divisible by j for all j in {1,2,3}.

0, 0, 0, 0, 5, 6, 18, 33, 50, 67, 115, 134, 206, 258, 340, 398, 537, 598, 778, 891, 1086, 1209, 1487, 1614, 1950, 2148, 2504, 2716, 3181, 3398, 3938, 4245, 4810, 5135, 5835, 6166, 6958, 7398, 8220, 8682, 9665, 10134, 11226, 11823, 12950, 13573, 14887, 15518

Offset

0,5

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (1,1,-1,0,0,2,-2,-2,2,0,0,-1,1,1,-1).

Formula

G.f.: (2*x^11+5*x^9+10*x^8+21*x^6+2*x^5+5*x^4+14*x^3+7*x^2+x+5)*x^4 / ((x^2+x+1)^2 *(x^2-x+1)^2 *(x+1)^3 *(x-1)^4).

Example

a(4) = 5: 102, 120, 123, 201, 321 (written in base 4).
a(5) = 6: 132, 201, 204, 314, 402, 421 (written in base 5).
a(6) = 18: 103, 120, 123, 140, 143, 203, 240, 243, 320, 340, 403, 420, 423, 503, 520, 523, 540, 543 (written in base 6).

Crossrefs

Column k=3 of A334318.

Sequence in context: A192727 A056519 A295972 * A063445 A257331 A240400

Adjacent sequences: A333402 A333403 A333404 * A333406 A333407 A333408

Keyword

nonn,easy

Author

Alois P. Heinz, May 04 2020

Status

approved