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A176476 Partial sums of A012814. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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).

LINKS

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (6,-9,5,-1).

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)

EXAMPLE

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

PROG

(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

CROSSREFS

Cf. A000931, A012814, A012855, A060006.

Sequence in context: A220101 A014825 A141844 * A079742 A291232 A171475

Adjacent sequences:  A176473 A176474 A176475 * A176477 A176478 A176479

KEYWORD

nonn,easy

AUTHOR

Carmine Suriano, Apr 18 2010

EXTENSIONS

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

STATUS

approved

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Last modified July 22 16:42 EDT 2019. Contains 325225 sequences. (Running on oeis4.)