A364135 - OEIS

A364135

Let d_r d_{r-1} ... d_1 d_0 be the decimal expansion of n; a(n) is the number of nonnegative integer solutions x_r ... x_0 to the Diophantine equation d_r*x_r + ... + d_0*x_0 = n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 12, 7, 5, 4, 4, 3, 3, 3, 3, 1, 11, 12, 4, 7, 3, 5, 2, 4, 2, 1, 11, 6, 12, 3, 3, 7, 2, 2, 5, 1, 11, 11, 4, 12, 3, 4, 2, 7, 2, 1, 11, 6, 4, 3, 12, 2, 2, 2, 2, 1, 11, 11, 11, 6, 3, 12, 2, 3, 4, 1, 11, 6, 4, 3, 3, 2, 12, 2, 2, 1, 11, 11

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OFFSET

1,11

COMMENTS

For a formula for a(n), please see the Samsonadze article in Links section. a(n) = P(b) if n = b AND the nonzero digits of b are the coefficients a_i (in the article).

a(n) is the number of partitions of n into parts that are nonzero digits of n. - Stefano Spezia, Feb 17 2024

LINKS

Robert P. P. McKone, Table of n, a(n) for n = 1..636

Eteri Samsonadze, On the number of integer non-negative solutions of a linear Diophantine equation, arXiv:2108.04756 [math.NT], 2021.

FORMULA

a(n) = 1 for n = (d 0 ... 0), the digit d >= 1, the number of zeros >= 0.

a(n) = (1 ... 1) + 1 for n = (d ... d), the digit d >= 1, n >= 10.

EXAMPLE

For n = 10: 1*x_1 + 0*x_0 = 10, the solution is x_1 = 10, thus a(10) = 1.

For n = 22: 2*x_1 + 2*x_0 = 22, the solutions are (0,11), (2,10), ..., (11,0), thus a(22) = 12.

MATHEMATICA

a[n_Integer] := Module[{ds = IntegerDigits[n], p, t, v}, p = Table[If[d == 0, {0}, Range[0, Quotient[n, d]]], {d, ds}]; t = Tuples[p]; v = Select[t, ds . # == n &]; Length[v]]; Table[a[n], {n, 1, 82}] (* Robert P. P. McKone, Aug 25 2023 *)

a[n_]:=Length[IntegerPartitions[n, All, DeleteCases[ IntegerDigits[n], 0]]]; Array[a, 82] (* Stefano Spezia, Feb 17 2024 *)

CROSSREFS

Cf. A007954, A034838, A052423, A055642.

Sequence in context: A002548 A363151 A359632 * A305939 A206423 A319406

Adjacent sequences: A364132 A364133 A364134 * A364136 A364137 A364138

KEYWORD

base,look,nonn

AUTHOR

Ctibor O. Zizka, Jul 10 2023

STATUS

approved