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%I #20 Oct 09 2020 03:50:35
%S 0,1,2,3,4,10,11,12,13,14,20,21,22,23,24,25,26,27,28,29,35,36,37,38,
%T 39,45,46,47,48,49,50,51,52,53,54,60,61,62,63,64,70,71,72,73,74,75,76,
%U 77,78,79,85,86,87,88,89,95,96,97,98,99,100,101,102,103,104,110,111,112
%N Numbers congruent to {0,1,2,3,4,10,11,12,13,14,20,21,22,23,24} mod 25.
%C 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.
%C For each number the partition is unique.
%C Complement of A174138.
%C 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).
%C 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).
%C First differs from A032955 at n = 76. - _Avi Mehra_, Oct 08 2020
%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(15+n) = a(n) + 25 for n >= 1.
%F From _R. J. Mathar_, Oct 08 2011: (Start)
%F a(n) = +a(n-1) +a(n-15) -a(n-16).
%F 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)
%t Select[Range[0, 112], Mod[Mod[#, 25], 10] < 5 &] (* _Amiram Eldar_, Oct 08 2020 *)
%o (PARI) { my(table=[0,1,2,3,4, 10,11,12,13,14, 20,21,22,23,24]);
%o a(n) = my(r);[n,r]=divrem(n-1,15); 25*n + table[r+1]; } \\ _Kevin Ryde_, Oct 08 2020
%Y 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).
%K easy,nonn
%O 1,3
%A _Rick L. Shepherd_, Mar 09 2010
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