OFFSET
0,2
COMMENTS
The tallied terms (A343524) are palindromes with digits strictly increasing up to the midpoint.
LINKS
FORMULA
a(n) = 1023 for n >= 18. - Michael S. Branicky, Jan 22 2024
a(n) = Sum_{k=1..n+1} binomial(9,floor(k/2)). - Andrew Howroyd, Jan 22 2024
G.f.: (-x^18 - x^17 - 9*x^16 - 9*x^15 - 36*x^14 - 36*x^13 - 84*x^12 - 84*x^11 - 126*x^10 - 126*x^9 - 126*x^8 - 126*x^7 - 84*x^6 - 84*x^5 - 36*x^4 - 36*x^3 - 9*x^2 - 9*x - 1)/(x - 1). - Chai Wah Wu, Jun 15 2024
EXAMPLE
PROG
(PARI) a(n)=sum(k=1, min(n, 18)+1, binomial(9, k\2)) \\ Andrew Howroyd, Jan 22 2024
(Python)
from math import comb
def a(n):
if n > 18: return 1023
return 1+sum(comb(9, (digits+1)//2) for digits in range(1, n+1))
print([a(n) for n in range(47)]) # Michael S. Branicky, Jan 22 2024
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
James S. DeArmon, Jan 19 2024
EXTENSIONS
a(11) and beyond from Michael S. Branicky, Jan 22 2024
STATUS
approved