

A174141


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


4



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
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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 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 wholedollar amounts is permitted or not).


LINKS

Table of n, a(n) for n=1..65.
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).


FORMULA

a(n+10) = a(n) + 25 for n >= 1.
a(n)= +a(n1) +a(n10) a(n11). 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^4x^3+x^2x+1)*(x1)^2 ).  R. J. Mathar, Oct 08 2011


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 *)


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).
Sequence in context: A068189 A069716 A095289 * A095706 A280249 A096867
Adjacent sequences: A174138 A174139 A174140 * A174142 A174143 A174144


KEYWORD

easy,nonn


AUTHOR

Rick L. Shepherd, Mar 09 2010


STATUS

approved



