A176476 Partial sums of A012814.

0, 1, 6, 27, 113, 464, 1896, 7738, 31571, 128800, 525455, 2143647, 8745216, 35676948, 145547524, 593775045, 2422362078, 9882257735, 40315615409, 164471408184, 670976837020, 2737314167774, 11167134898975, 45557394660800, 185855747875875, 758216295635151

Offset: 0

Author

Carmine Suriano, Apr 18 2010

Keywords

• nonn
• easy

Comments

Old name was "a(n) is the minimum integer that can be expressed as the sum of n Padovan numbers (see A000931)".

Lim_{n -> infinity} a(n+1)/a(n) = p^5 = 4.0795956..., where p is the plastic constant (A060006).

Examples

			a(5) = A000931(2) + A000931(7) + A000931(12) + A000931(17) + A000931(22) + A000931(27) = 0 + 1 + 5 + 21 + 86 + 351 = 464.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..1638
• Sela Fried, Even-up words and their variants, arXiv:2505.14196 [math.CO], 2025. See p. 7.
• Index entries for linear recurrences with constant coefficients, signature (6,-9,5,-1).

Crossrefs

Cf. A000931, A012814, A012855, A060006.

Programs

Mathematica

LinearRecurrence[{6,-9,5,-1},{0,1,6,27},30] (* Harvey P. Dale, Feb 08 2025 *)

PARI

a(n) = my(v=vector(n+1), u=[0,1,6,27]); for(k=1, n+1, v[k]=if(k<=4, u[k], 5*v[k-1] - 4*v[k-2] + v[k-3] + 1)); v[n+1] \\ Jianing Song, Feb 04 2019

Formula

a(n) = A012855(n+3) - 1. a(n) = 6*a(n-1) - 9*a(n-2) + 5*a(n-3) - a(n-4). - R. J. Mathar, Oct 18 2010

G.f.: x/(1 - 6*x + 9*x^2 - 5*x^3 + x^4). - Colin Barker, Feb 03 2012

From Jianing Song, Feb 04 2019: (Start)

a(n+3) = 5*a(n+2) - 4*a(n+1) + a(n) + 1.

a(n) = Sum_{k=0..n} A012814(k) = Sum_{k=0..n} A000931(5*k+2). (End)

Extensions

New name, more terms and a(0) = 0 prepended by Jianing Song, Feb 04 2019