A351726 -id:A351726 - cp's OEIS frontend

A351724 Number of compositions of n into parts of size 1, 5, 10 or 25.

1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 9, 13, 18, 24, 31, 42, 58, 80, 109, 146, 197, 268, 366, 499, 676, 916, 1243, 1690, 2299, 3122, 4237, 5751, 7811, 10614, 14418, 19580, 26587, 36106, 49043, 66614, 90473, 122869, 166866, 226632, 307810, 418060, 567784, 771122, 1047296, 1422396, 1931845

Offset: 0

R. J. Mathar, Feb 17 2022

Starts to differ from A114044 at n=50.

			a(8)=5 counts 5 compositions 1+1+1+1+1+1+1+1 = 1+1+1+5 = 1+1+5+1 = 1+5+1+1 = 5+1+1+1.

Index entries for sequences related to making change.
Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Cf. A114044 (parts 50 and 100 admitted), A001299 (partitions).

Row sums of A351726.

G.f. : 1/(1-x-x^5-x^10-x^25).

a(n) = +a(n-1) +a(n-5) +a(n-10) +a(n-25).

A358131 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).

Original entry on oeis.org

0, 25, 10, 50, 35, 20, 75, 60, 45, 30, 100, 85, 70, 55, 40, 125, 110, 95, 80, 65, 50, 150, 135, 120, 105, 90, 75, 60, 175, 160, 145, 130, 115, 100, 85, 70, 200, 185, 170, 155, 140, 125, 110, 95, 80, 225, 210, 195, 180, 165, 150, 135, 120, 105, 90, 250, 235, 220, 205, 190

Offset: 0

Wesley Ivan Hurt, Oct 30 2022

			Triangle begins
  n\k |   0    1    2    3    4    5    6    7    8    9   10
  ----|----------------------------------------------------------
   0  |   0
   1  |  25   10
   2  |  50   35   20
   3  |  75   60   45   30
   4  | 100   85   70   55   40
   5  | 125  110   95   80   65   50
   6  | 150  135  120  105   90   75   60
   7  | 175  160  145  130  115  100   85   70
   8  | 200  185  170  155  140  125  110   95   80
   9  | 225  210  195  180  165  150  135  120  105   90
  10  | 250  235  220  205  190  175  160  145  130  115  100
  ...

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

Cf. A351726.

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

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

cp's OEIS Frontend

A351724 Number of compositions of n into parts of size 1, 5, 10 or 25.

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