A333469 Number of integers in base n having exactly four distinct digits such that the number formed by the consecutive subsequence of the initial j digits is divisible by j for all j in {1,2,3,4}.

0, 0, 0, 0, 2, 1, 8, 34, 58, 98, 168, 275, 428, 586, 849, 1193, 1647, 2017, 2679, 3454, 4410, 5283, 6676, 7900, 9838, 11396, 13758, 15994, 19216, 21493, 25450, 29026, 33854, 37636, 43724, 48369, 55884, 61374, 69831, 76803, 87269, 94285, 106337, 116062, 129862

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,-1,0,0,0,0,0,0,0,0,3,-3,-3,3,0,0,0,0,0,0,0,0,-3,3,3,-3,0,0,0,0,0,0,0,0,1,-1,-1,1).

Formula

G.f.: -(6*x^35 -4*x^33 +41*x^32 +11*x^31 +87*x^30 -46*x^29 +40*x^28 +165*x^27 +126*x^26 -40*x^25 +293*x^24 +120*x^23 +94*x^22 +181*x^21 +296*x^20 +150*x^19 +299*x^18 +56*x^17 +243*x^16 +324*x^15 +193*x^14 +29*x^13 +185*x^12 +186*x^11 +110*x^10 +51*x^9 +83*x^8 +67*x^7 +46*x^6 +14*x^5 +17*x^4 +27*x^3 +5*x^2 -x +2)*x^4 / ((x^2+1)^3 *(x^2+x+1)^3 *(x^2-x+1)^3 *(x^4-x^2+1)^3 *(x+1)^4 *(x-1)^5).

Example

a(4) = 2: 1230, 3210 (written in base 4).
a(5) = 1: 3140 (written in base 5).
a(6) = 6: 1032, 1204, 1432, 3204, 4032, 5032, 5204, 5432 (written in base 6).

Mathematica

LinearRecurrence[{1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 3, -3, -3, 3, 0, 0, 0, 0, 0, 0, 0, 0, -3, 3, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1}, {0, 0, 0, 0, 2, 1, 8, 34, 58, 98, 168, 275, 428, 586, 849, 1193, 1647, 2017, 2679, 3454, 4410, 5283, 6676, 7900, 9838, 11396, 13758, 15994, 19216, 21493, 25450, 29026, 33854, 37636, 43724, 48369, 55884, 61374, 69831, 76803}, 110] (* Harvey P. Dale, Oct 06 2023 *)

Crossrefs

Column k=4 of A334318.

Sequence in context: A012962 A214731 A079899 * A239444 A224090 A013327

Adjacent sequences: A333466 A333467 A333468 * A333470 A333471 A333472

Keyword

nonn,easy

Author

Alois P. Heinz, May 04 2020

Status

approved