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

Author

Laurent Desnogues and Charles R Greathouse IV, Apr 02 2012

Keywords

• nonn
• base
• easy

Comments

Different from A016135.

Examples

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

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).

Crossrefs

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

Programs

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

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

Extensions

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