A358131 - OEIS

%I #12 Nov 10 2022 16:12:27

%S 0,25,10,50,35,20,75,60,45,30,100,85,70,55,40,125,110,95,80,65,50,150,

%T 135,120,105,90,75,60,175,160,145,130,115,100,85,70,200,185,170,155,

%U 140,125,110,95,80,225,210,195,180,165,150,135,120,105,90,250,235,220,205,190

%N Triangle T(n,k) read by rows, where each row lists the value of n coins, in cents, using k dimes (10 cents) and n-k quarters (25 cents).

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Change-making_problem">Change-making problem</a>

%H <a href="/index/Mag#change">Index entries for sequences related to making change.</a>

%F T(n,k) = 10*k + 25*(n-k), 0 <= k <= n.

%e Triangle begins

%e   n\k |   0    1    2    3    4    5    6    7    8    9   10

%e   ----|----------------------------------------------------------

%e    0  |   0

%e    1  |  25   10

%e    2  |  50   35   20

%e    3  |  75   60   45   30

%e    4  | 100   85   70   55   40

%e    5  | 125  110   95   80   65   50

%e    6  | 150  135  120  105   90   75   60

%e    7  | 175  160  145  130  115  100   85   70

%e    8  | 200  185  170  155  140  125  110   95   80

%e    9  | 225  210  195  180  165  150  135  120  105   90

%e   10  | 250  235  220  205  190  175  160  145  130  115  100

%e   ...

%t T[n_, k_] := T[n, k] = 10 k + 25 (n - k); Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten

%Y Cf. A008592 (right diagonal), A008607 (1st column).

%Y Cf. A351726.

%K nonn,easy,tabl

%O 0,2

%A _Wesley Ivan Hurt_, Oct 30 2022