A211072 Sum of numbers with no '0' decimal digits whose sum of digits equals n.

0, 1, 13, 147, 1625, 17891, 196833, 2165227, 23817625, 261994131, 2881935943, 31701296375, 348714262017, 3835856884757, 42194425724149, 464138682802857, 5105525508895321, 56160780576260645, 617768586100819485, 6795454444489330049, 74749998860563784655

Offset

0,3

Comments

Different from A016135.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..961 (terms n = 1..31 from Laurent Desnogues)

Project Euler, Problem 377: Sum of digits, experience 13

Tadao Takaoku, A two-level algorithm for generating multiset permutations, RIMS Kokyuroku 1644 (2009), pp. 95-109.

Index entries for linear recurrences with constant coefficients, signature (11,1,-9,-19,-29,-39,-49,-59,-69,-90,-80,-70,-60,-50,-40,-30,-20,-10).

Formula

G.f.: x*(9*x^8 + 8*x^7 + 7*x^6 + 6*x^5 + 5*x^4 + 4*x^3 + 3*x^2 + 2*x + 1)/((x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x - 1)*(10*x^9 + 10*x^8 + 10*x^7 + 10*x^6 + 10*x^5 + 10*x^4 + 10*x^3 + 10*x^2 + 10*x - 1)). - Yurii Ivanov, Jul 06 2021

Example

2 and 11 are the only numbers without 0's which have digit sum 2, so a(2) = 2 + 11 = 13.

Maple

b:= proc(n) option remember; `if`(n=0, [1, 0], add((p->
      [p[1], p[2]*10+p[1]*d])(b(n-d)), d=1..min(n, 9)))
    end:
a:= n-> b(n)[2]:
seq(a(n), n=0..23);  # Alois P. Heinz, Feb 19 2020

Crossrefs

Cf. A007953, A016135, A052382, A130835, A258800.

Sequence in context: A353107 A051524 A110748 * A016135 A332691 A210165

Adjacent sequences: A211069 A211070 A211071 * A211073 A211074 A211075

Keyword

nonn,base,easy

Author

Laurent Desnogues and Charles R Greathouse IV, Apr 02 2012

Extensions

a(0)=0 prepended by Alois P. Heinz, Feb 19 2020

Status

approved