OFFSET
1,3
COMMENTS
Numbers whose partition into parts of sizes 1, 5, 10, and 25 having a minimal number of parts does not include a part of size 5.
For each number the partition is unique.
Complement of A174138.
Amounts in cents not including a nickel when the minimal number of coins is selected from pennies, nickels, dimes, and quarters (whether usage of bills for whole-dollar amounts is permitted or not).
For each n >= 0, floor(n/25) parts of size 25 (quarters) occur in the partition with minimal number of these parts (regardless of whether partition includes part of size 5).
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1).
FORMULA
a(15+n) = a(n) + 25 for n >= 1.
From R. J. Mathar, Oct 08 2011: (Start)
a(n) = +a(n-1) +a(n-15) -a(n-16).
G.f.: x^2*(1 +x +x^2 +x^3 +6*x^4 +x^5 +x^6 +x^7 +x^8 +6*x^9 +x^10 +x^11 +x^12 +x^13+x^14) / ( (1+x+x^2) *(x^4+x^3+x^2+x+1) *(x^8-x^7+x^5-x^4+x^3-x+1) *(x-1)^2). (End)
MATHEMATICA
Select[Range[0, 112], Mod[Mod[#, 25], 10] < 5 &] (* Amiram Eldar, Oct 08 2020 *)
PROG
(PARI) { my(table=[0, 1, 2, 3, 4, 10, 11, 12, 13, 14, 20, 21, 22, 23, 24]);
a(n) = my(r); [n, r]=divrem(n-1, 15); 25*n + table[r+1]; } \\ Kevin Ryde, Oct 08 2020
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Rick L. Shepherd, Mar 09 2010
STATUS
approved