OFFSET
1,1
COMMENTS
An infinite subsequence of A003052.
LINKS
Shyam Sunder Gupta, On Some Marvellous Numbers of Kaprekar, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 9, pp. 275-315.
Bernardo Recamán and D. W. Bange, Solution to Problem E 2408, Amer. Math. Monthly, Vol. 81, No. 4 (1974), p. 407.
Index entries for linear recurrences with constant coefficients, signature (12,-21,10).
FORMULA
From R. J. Mathar, Nov 24 2013: (Start)
G.f.: x*(-9+11*x+70*x^2) / ((10*x-1)*(x-1)^2).
a(n) = (8*10^n-71)/9+8*n. (End)
From Elmo R. Oliveira, Aug 22 2026: (Start)
E.g.f.: (1/9)*(63 + (72*x - 71)*exp(x) + 8*exp(10*x)).
a(n) = 12*a(n-1) - 21*a(n-2) + 10*a(n-3).
MAPLE
f:=proc(n) option remember; if n=1 then 9 else
8*10^(n-1)+8+f(n-1); fi; end;
[seq(f(n), n=1..40)];
MATHEMATICA
RecurrenceTable[{a[1]==9, a[n]==8*10^(n-1)+8+a[n-1]}, a, {n, 30}] (* Harvey P. Dale, May 19 2018 *)
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
N. J. A. Sloane, Nov 22 2013
EXTENSIONS
Definition corrected by Harvey P. Dale, May 19 2018
STATUS
approved