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A176476 Partial sums of A012814.

%I A176476 #46 May 30 2025 10:33:51
%S A176476 0,1,6,27,113,464,1896,7738,31571,128800,525455,2143647,8745216,
%T A176476 35676948,145547524,593775045,2422362078,9882257735,40315615409,
%U A176476 164471408184,670976837020,2737314167774,11167134898975,45557394660800,185855747875875,758216295635151
%N A176476 Partial sums of A012814.
%C A176476 Old name was "a(n) is the minimum integer that can be expressed as the sum of n Padovan numbers (see A000931)".
%C A176476 Lim_{n -> infinity} a(n+1)/a(n) = p^5 = 4.0795956..., where p is the plastic constant (A060006).
%H A176476 Michael De Vlieger, <a href="/A176476/b176476.txt">Table of n, a(n) for n = 0..1638</a>
%H A176476 Sela Fried, <a href="https://arxiv.org/abs/2505.14196">Even-up words and their variants</a>, arXiv:2505.14196 [math.CO], 2025. See p. 7.
%H A176476 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-9,5,-1).
%F A176476 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
%F A176476 G.f.: x/(1 - 6*x + 9*x^2 - 5*x^3 + x^4). - _Colin Barker_, Feb 03 2012
%F A176476 From _Jianing Song_, Feb 04 2019: (Start)
%F A176476 a(n+3) = 5*a(n+2) - 4*a(n+1) + a(n) + 1.
%F A176476 a(n) = Sum_{k=0..n} A012814(k) = Sum_{k=0..n} A000931(5*k+2). (End)
%e A176476 a(5) = A000931(2) + A000931(7) + A000931(12) + A000931(17) + A000931(22) + A000931(27) = 0 + 1 + 5 + 21 + 86 + 351 = 464.
%t A176476 LinearRecurrence[{6,-9,5,-1},{0,1,6,27},30] (* _Harvey P. Dale_, Feb 08 2025 *)
%o A176476 (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
%Y A176476 Cf. A000931, A012814, A012855, A060006.
%K A176476 nonn,easy
%O A176476 0,3
%A A176476 _Carmine Suriano_, Apr 18 2010
%E A176476 New name, more terms and a(0) = 0 prepended by _Jianing Song_, Feb 04 2019