%I #15 Mar 17 2022 08:42:39
%S 10,20,25,35,45,50,60,70,75,85,95,100,110,120,125,135,145,150,160,170,
%T 175,185,195,200,210,220,225,235,245,250,260,270,275,285,295,300,310,
%U 320,325,335,345,350,360,370,375,385,395,400,410,420,425,435,445,450,460,470,475,485,495,500,510,520,525,535,545,550,560
%N Monetary amounts in U.S. cents such that the smallest number of coins summing to the amount uses only denominations of 10 cents and above.
%C U.S. coins are the cent ("penny") (1 cent), nickel (5 cents), dime (10 cents), quarter dollar ("quarter") (25 cents), half dollar (50 cents), and dollar (100 cents).
%C For values above 100, one can simply add 100 to the previous terms: a(n) = a(n-12) + 100. - _R. J. Mathar_, Aug 05 2010
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F From _R. J. Mathar_, Aug 05 2010: (Start)
%F a(n) = +a(n-1) +a(n-3) -a(n-4).
%F G.f.: 5*x*(2+2*x+x^2) / ( (1+x+x^2)*(x-1)^2 ). (End)
%e A total amount of 30 cents can be obtained using 3 coins as 10+10+10, but the only way to obtain 30 cents using 2 coins (which is the minimum number of coins) is as 25+5 (which includes a coin smaller than a 10-cent piece), so 30 is not in the sequence.
%e From _R. J. Mathar_, Aug 05 2010: (Start)
%e Shortest partitions of multiples of 5 into parts of 5, 10, 25, 50, 100:
%e 5 = 5
%e 10 = 10 a(1)
%e 15 = 5 + 10
%e 20 = 10 + 10 a(2)
%e 25 = 25 a(3)
%e 30 = 5 + 25
%e 35 = 10 + 25 a(4)
%e 40 = 5 + 10 + 25
%e 45 = 10 + 10 + 25 a(5)
%e 50 = 50 a(6)
%e 55 = 5 + 50
%e 60 = 10 + 50 a(7)
%e 65 = 5 + 10 + 50
%e 70 = 10 + 10 + 50 a(8)
%e 75 = 25 + 50 a(9)
%e 80 = 5 + 25 + 50
%e 85 = 10 + 25 + 50 a(10)
%e 90 = 5 + 10 + 25 + 50
%e 95 = 10 + 10 + 25 + 50 a(11)
%e 100 = 100. a(12)
%e (End)
%K nonn,easy
%O 1,1
%A _J. Lowell_, Jul 28 2010
%E More terms from _R. J. Mathar_, Aug 05 2010
%E More terms from _Max Alekseyev_, Oct 15 2012