A174139 Numbers congruent to {0,1,2,3,4,10,11,12,13,14,20,21,22,23,24} mod 25.

0, 1, 2, 3, 4, 10, 11, 12, 13, 14, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 35, 36, 37, 38, 39, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 60, 61, 62, 63, 64, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 85, 86, 87, 88, 89, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 110, 111, 112

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 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).

First differs from A032955 at n = 76. - Avi Mehra, Oct 08 2020

Links

• 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, A174140, 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

Select[Range[0, 112], Mod[Mod[#, 25], 10] < 5 &] (* Amiram Eldar, Oct 08 2020 *)

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

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)