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A316966 Same as A316671, except numbering of the squares starts at 0 rather than 1. 1

%I #20 Jan 22 2022 16:43:27

%S 0,4,3,11,10,22,21,37,36,56,55,79,78,106,105,137,136,172,171,211,210,

%T 254,253,301,300,352,351,407,406,466,465,529,528,596,595,667,666,742,

%U 741,821,820,904,903,991,990,1082,1081,1177,1176,1276,1275,1379,1378

%N Same as A316671, except numbering of the squares starts at 0 rather than 1.

%C See A316671 for further information.

%H Daniël Karssen, <a href="/A316966/b316966.txt">Table of n, a(n) for n = 0..9999</a>

%H Daniël Karssen, <a href="/A316966/a316966.svg">Figure showing the first 6 steps of the sequence</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).

%F a(n) = A316671(n+1) - 1.

%F From _Colin Barker_, Jul 19 2018: (Start)

%F G.f.: x*(4 - x + x^3) / ((1 - x)^3*(1 + x)^2).

%F a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n>4. (End)

%F a(n) = 1 + (n + 2)*(n - (-1)^n)/2. - _Bruno Berselli_, Jul 19 2018

%t Table[1 + (n + 2) (n - (-1)^n)/2, {n, 0, 60}] (* _Bruno Berselli_, Jul 19 2018 *)

%o (PARI) concat(0, Vec(x*(4 - x + x^3) / ((1 - x)^3*(1 + x)^2) + O(x^40))) \\ _Colin Barker_, Jul 19 2018

%Y Cf. A316671.

%Y Cf. A128918: it is provided by a(-n-1).

%K nonn,easy

%O 0,2

%A _Daniël Karssen_, Jul 17 2018

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Last modified March 28 13:19 EDT 2024. Contains 371254 sequences. (Running on oeis4.)