This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A118729 #65 Sep 13 2024 03:33:33
%S A118729 0,0,0,0,0,0,0,0,1,2,3,4,5,6,7,8,10,12,14,16,18,20,22,24,27,30,33,36,
%T A118729 39,42,45,48,52,56,60,64,68,72,76,80,85,90,95,100,105,110,115,120,126,
%U A118729 132,138,144,150,156,162,168
%N A118729 Rectangular array where row r contains the 8 numbers 4*r^2 - 3*r, 4*r^2 - 2*r, ..., 4*r^2 + 4*r.
%C A118729 The numbers in row r span the interval ]8*A000217(r-1), 8*A000217(r)].
%C A118729 The first difference between the entries in row r is r.
%C A118729 Partial sums of floor(n/8). - _Philippe Deléham_, Mar 26 2013
%C A118729 Apart from the initial zeros, the same as A008726. - _Philippe Deléham_, Mar 28 2013
%C A118729 a(n+7) is the number of key presses required to type a word of n letters, all different, on a keypad with 8 keys where 1 press of a key is some letter, 2 presses is some other letter, etc., and under an optimal mapping of letters to keys and presses (answering LeetCode problem 3014). - _Christopher J. Thomas_, Feb 16 2024
%H A118729 G. C. Greubel, <a href="/A118729/b118729.txt">Table of n, a(n) for n = 0..1000</a>
%H A118729 LeetCode, <a href="https://leetcode.com/problems/minimum-number-of-pushes-to-type-word-i">3014. Minimum Number of Pushes to Type Word I</a>.
%H A118729 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,0,0,0,1,-2,1).
%F A118729 From _Philippe Deléham_, Mar 26 2013: (Start)
%F A118729 a(8k) = A001107(k).
%F A118729 a(8k+1) = A002939(k).
%F A118729 a(8k+2) = A033991(k).
%F A118729 a(8k+3) = A016742(k).
%F A118729 a(8k+4) = A007742(k).
%F A118729 a(8k+5) = A002943(k).
%F A118729 a(8k+6) = A033954(k).
%F A118729 a(8k+7) = A033996(k). (End)
%F A118729 G.f.: x^8/((1-x)^2*(1-x^8)). - _Philippe Deléham_, Mar 28 2013
%F A118729 a(n) = floor(n/8)*(n-3-4*floor(n/8)). - _Ridouane Oudra_, Jun 04 2019
%F A118729 a(n+7) = (1/2)*(n+(n mod 8))*(floor(n/8)+1). - _Christopher J. Thomas_, Feb 13 2024
%e A118729 The array starts, with row r=0, as
%e A118729 r=0: 0 0 0 0 0 0 0 0;
%e A118729 r=1: 1 2 3 4 5 6 7 8;
%e A118729 r=2: 10 12 14 16 18 20 22 24;
%e A118729 r=3: 27 30 33 36 39 42 45 48;
%t A118729 Flatten[Table[4r^2+r(Range[-3,4]),{r,0,6}]] (* or *) LinearRecurrence[ {2,-1,0,0,0,0,0,1,-2,1},{0,0,0,0,0,0,0,0,1,2},60] (* _Harvey P. Dale_, Nov 26 2015 *)
%Y A118729 Cf. similar sequences: A000217, A002620, A130518, A130519, A130520, A174709, A174738, A218470, A131242.
%K A118729 nonn,tabf,easy
%O A118729 0,10
%A A118729 Stuart M. Ellerstein (ellerstein(AT)aol.com), May 21 2006
%E A118729 Redefined as a rectangular tabf array and description simplified by _R. J. Mathar_, Oct 20 2010