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%I #10 Aug 01 2015 08:50:45
%S 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,
%T 56,57,58,59,75,76,77,78,79,80,81,82,83,84,100,101,102,103,104,105,
%U 106,107,108,109,125,126,127,128,129,130,131,132,133,134,150,151,152,153,154
%N Numbers congruent to k mod 25, where 0 <= k <= 9.
%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 10.
%C For each number the partition is unique.
%C Complement of A174140.
%C 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 whole-dollar amounts is permitted or not).
%H <a href="/index/Mag#change">Index entries for sequences related to making change.</a>
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).
%F a(n+10) = a(n) + 25 for n >= 1.
%F a(n)= +a(n-1) +a(n-10) -a(n-11). 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^4-x^3+x^2-x+1)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011
%t 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 *)
%Y 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).
%K easy,nonn
%O 1,3
%A _Rick L. Shepherd_, Mar 09 2010
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