A383942 - OEIS

A383942

a(n) = (8*10^(2n) - 10^(n+1) + 2) / 9.

78, 8778, 887778, 88877778, 8888777778, 888887777778, 88888877777778, 8888888777777778, 888888887777777778, 88888888877777777778, 8888888888777777777778, 888888888887777777777778, 88888888888877777777777778, 8888888888888777777777777778

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OFFSET

1,1

COMMENTS

This is one of four infinite families of triangular numbers consisting of two different digits. The other three families are A319170, A037156 (n>1), and A309597 (n>2).

LINKS

Paolo Xausa, Table of n, a(n) for n = 1..495

Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

FORMULA

a(n) = A000217(A073551(n+1)).

G.f.: 6*x*(13 + 20*x)/((1 - x)*(1 - 10*x)*(1 - 100*x)). - Stefano Spezia, Aug 19 2025

MATHEMATICA

A383942[n_] := (8*10^(2*n) - 10^(n+1) + 2)/9; Array[A383942, 15] (* or *)

LinearRecurrence[{111, -1110, 1000}, {78, 8778, 887778}, 15] (* Paolo Xausa, Aug 27 2025 *)

PROG

(Python) def A383942(n): return (8*10**(2*n)-10**(n+1)+2)//9

CROSSREFS