A174141 Numbers congruent to k mod 25, where 0 <= k <= 9.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 150, 151, 152, 153, 154

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 10.

For each number the partition is unique.

Complement of A174140.

Amounts in cents not including a 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

• 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, 1, -1).

Crossrefs

Cf. A174138, A174139, A174140, A047201 (requires at least one part of size 1 (penny)), A008587, A053344 (minimal number of parts), A001299 (number of all such partitions).

Programs

Mathematica

LinearRecurrence[{1,0,0,0,0,0,0,0,0,1,-1},{0,1,2,3,4,5,6,7,8,9,25},70] (* Harvey P. Dale, May 30 2014 *)

Formula

a(n+10) = a(n) + 25 for n >= 1.

a(n)= +a(n-1) +a(n-10) -a(n-11). G.f. x^2*(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+16*x^9) / ( (1+x)*(1+x+x^2+x^3+x^4)*(x^4-x^3+x^2-x+1)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011