A174140 Numbers congruent to k mod 25, where 10 <= k <= 24.

10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 110, 111, 112, 113, 114, 115, 116

Offset: 1

Author

Rick L. Shepherd, Mar 09 2010

Keywords

• easy
• nonn

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 sequences related to making change.
• 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).

Crossrefs

Cf. A174138, A174139, A174141, A047201 (requires at least one part of size 1 (penny)), A008587, A053344 (minimal number of parts), A001299 (number of all such partitions).

Programs

Mathematica

Flatten[Table[Range[10,24]+25n,{n,0,5}]] (* Harvey P. Dale, Jun 12 2012 *)

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

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)