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A174139 Numbers congruent to {0,1,2,3,4,10,11,12,13,14,20,21,22,23,24} mod 25. 3
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 (list; graph; refs; listen; history; text; internal format)
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 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

Table of n, a(n) for n=1..68.

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).

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)

MATHEMATICA

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

PROG

(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

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).

Sequence in context: A119798 A015976 A098892 * A037325 A293292 A037469

Adjacent sequences:  A174136 A174137 A174138 * A174140 A174141 A174142

KEYWORD

easy,nonn

AUTHOR

Rick L. Shepherd, Mar 09 2010

STATUS

approved

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Last modified September 21 16:31 EDT 2021. Contains 347598 sequences. (Running on oeis4.)