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A174140 Numbers congruent to k mod 25, where 10 <= k <= 24. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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
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(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)
MATHEMATICA
Flatten[Table[Range[10, 24]+25n, {n, 0, 5}]] (* Harvey P. Dale, Jun 12 2012 *)
PROG
(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
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).
Sequence in context: A117884 A133506 A046510 * A357929 A322322 A038368
KEYWORD
easy,nonn
AUTHOR
Rick L. Shepherd, Mar 09 2010
STATUS
approved

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Last modified March 28 07:48 EDT 2024. Contains 371235 sequences. (Running on oeis4.)