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%I #10 Oct 25 2019 05:11:35
%S 10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,35,36,37,38,39,40,41,42,
%T 43,44,45,46,47,48,49,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,85,
%U 86,87,88,89,90,91,92,93,94,95,96,97,98,99,110,111,112,113,114,115,116
%N Numbers congruent to k mod 25, where 10 <= k <= 24.
%C 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.
%C For each number the partition is unique.
%C Complement of A174141.
%C 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).
%H Colin Barker, <a href="/A174140/b174140.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Mag#change">Index entries for sequences related to making change.</a>
%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1).
%F a(n+15) = a(n) + 25 for n >= 1.
%F From _Colin Barker_, Oct 25 2019: (Start)
%F 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)).
%F a(n) = a(n-1) + a(n-15) - a(n-16) for n>16.
%F (End)
%t Flatten[Table[Range[10,24]+25n,{n,0,5}]] (* _Harvey P. Dale_, Jun 12 2012 *)
%o (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
%Y 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).
%K easy,nonn
%O 1,1
%A _Rick L. Shepherd_, Mar 09 2010
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