A351726 - OEIS

A351726

Table T(n,k) read by rows: number of compositions of n into k parts of size 1, 5, 10 or 25.

1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, 1, 0, 0, 0, 0, 4, 0, 0, 0, 1, 0, 0, 0, 0, 0, 5, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 6, 0, 0, 0, 1, 0, 0, 2, 3, 0, 0, 0, 7, 0, 0, 0, 1, 0, 0, 0, 3, 6, 0, 0, 0, 8, 0, 0, 0, 1, 0, 0, 0, 0, 4

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OFFSET

0,24

LINKS

Table of n, a(n) for n=0..95.

L. Zhiwen, Expect coin value problem (a variant of coin exchange problem), math.stackexchange Feb 12, 2022.

Index entries for sequences related to making change.

FORMULA

T(n,0) = 0 if k>0.

G.f.: 1/(1-y*g(x)) where g(x)=x+x^5+x^10+x^25 is the g.f. of column k=1.

EXAMPLE

T(7,3)=3 counts 1+1+5 =1+5+1 =5+1+1.

T(10,2)=1 counts 5+5.

T(12,3)=3 counts 1+1+10 =1+10+1 =10+1+1.

T(15,3)=1 counts 5+5+5.

T(16,3)=6 counts 1+5+10 =1+10+5 =5+1+10 =5+10+1 =10+1+5 =10+5+1.

The triangle starts in row n=0 and columns 0<=k<=n:

0 1

0 0 1

0 0 0 1

0 0 0 0 1

0 1 0 0 0 1

0 0 2 0 0 0 1

0 0 0 3 0 0 0 1

0 0 0 0 4 0 0 0 1

0 0 0 0 0 5 0 0 0 1

0 1 1 0 0 0 6 0 0 0 1

0 0 2 3 0 0 0 7 0 0 0 1

0 0 0 3 6 0 0 0 8 0 0 0 1

0 0 0 0 4 10 0 0 0 9 0 0 0 1

0 0 0 0 0 5 15 0 0 0 10 0 0 0 1

0 0 2 1 0 0 6 21 0 0 0 11 0 0 0 1

0 0 0 6 4 0 0 7 28 0 0 0 12 0 0 0 1

0 0 0 0 12 10 0 0 8 36 0 0 0 13 0 0 0 1

0 0 0 0 0 20 20 0 0 9 45 0 0 0 14 0 0 0 1

0 0 0 0 0 0 30 35 0 0 10 55 0 0 0 15 0 0 0 1

0 0 1 3 1 0 0 42 56 0 0 11 66 0 0 0 16 0 0 0 1

0 0 0 3 12 5 0 0 56 84 0 0 12 78 0 0 0 17 0 0 0 1

0 0 0 0 6 30 15 0 0 72 120 0 0 13 91 0 0 0 18 0 0 0 1

CROSSREFS

Cf. A351724 (row sums), A351725 (partitions).

Sequence in context: A343221 A327169 A299173 * A285720 A269175 A086076

Adjacent sequences: A351723 A351724 A351725 * A351727 A351728 A351729

KEYWORD

nonn,easy,tabl

AUTHOR

R. J. Mathar, Feb 17 2022

STATUS

approved