OFFSET
1,3
COMMENTS
Published with slightly different wording in Mathematics Magazine, Problem 1016, Dec. 1977.
Analyzed for n = 1, 2, 3; computer-verified for n up to 8.
All solutions consist of an even number of digits followed by the digit 5 followed by zero or more 0's. This pattern means that a(2*n-1) = a(2*n). The initial segment consists of pairs of digits that add to 9 (0 with 9, 1 with 8, etc) arranged in arbitrary order and in particular leading 0's are permitted by the definition of the problem. A287317(k) gives the number of such arrangement with k pairs. For example, 339606500 + 660393500 is a solution. - Andrew Howroyd, Nov 03 2019
LINKS
Michael W. Ecker, Problem 1016, Mathematics Magazine, Vol. 50, No. 3 (May, 1977), pp. 163-169.
FORMULA
a(n) = Sum_{k=0..floor((n-1)/2)} A287317(k). - Andrew Howroyd, Nov 03 2019
EXAMPLE
For n = 3, solutions are (095, 905), (185, 815), (275, 725), (365, 635), (455, 545), (500, 500), (545, 455), (635, 365), (725, 275), (815, 185), (905, 095).
PROG
(PARI) seq(n)={Vec(serlaplace(besseli(0, 2*x + O(x*x^n))^5)/(1-x))} \\ Andrew Howroyd, Nov 03 2019
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Dr. Michael W. Ecker, Oct 30 2019
EXTENSIONS
Terms a(9) and beyond from Andrew Howroyd, Nov 03 2019
STATUS
approved