OFFSET
1,1
COMMENTS
Numbers whose partition into parts of sizes 1, 5, 10, and 25 having a minimal number of parts includes at least one part of size 10.
For each number the partition is unique.
Complement of A174141.
Amounts in cents requiring at least one dime 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).
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
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(n+15) = a(n) + 25 for n >= 1.
From Colin Barker, Oct 25 2019: (Start)
G.f.: x*(10 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10 + x^11 + x^12 + x^13 + x^14 + x^15) / ((1 - x)^2*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)*(1 - x + x^3 - x^4 + x^5 - x^7 + x^8)).
a(n) = a(n-1) + a(n-15) - a(n-16) for n>16.
(End)
MATHEMATICA
Flatten[Table[Range[10, 24]+25n, {n, 0, 5}]] (* Harvey P. Dale, Jun 12 2012 *)
PROG
(PARI) Vec(x*(10 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 + x^10 + x^11 + x^12 + x^13 + x^14 + x^15) / ((1 - x)^2*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)*(1 - x + x^3 - x^4 + x^5 - x^7 + x^8)) + O(x^60)) \\ Colin Barker, Oct 25 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Rick L. Shepherd, Mar 09 2010
STATUS
approved