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 A178827 #38 Dec 22 2023 10:34:17
%S A178827 0,1,9,74,594,4755,38043,304348,2434788,19478309,155826477,1246611822,
%T A178827 9972894582,79783156663,638265253311,5106122026496,40848976211976,
%U A178827 326791809695817,2614334477566545,20914675820532370,167317406564258970,1338539252514071771,10708314020112574179,85666512160900593444,685332097287204747564
%N A178827 Partial sums of floor(8^n/9)/7.
%H A178827 Bruno Berselli, <a href="/A178827/b178827.txt">Table of n, a(n) for n = 1..1000</a>
%H A178827 Mircea Merca, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL14/Merca/merca3.html">Inequalities and Identities Involving Sums of Integer Functions</a> J. Integer Sequences, Vol. 14 (2011), Article 11.9.1.
%H A178827 <a href="/index/Rec$order_04">Index entries for linear recurrences with constant coefficients</a>, signature (9,-7,-9,8).
%F A178827 7*a(n) = round((32*8^n - 126*n - 81)/252).
%F A178827 7*a(n) = floor((16*8^n - 63*n - 16)/126).
%F A178827 7*a(n) = ceiling((16*8^n - 63*n - 65)/126).
%F A178827 7*a(n) = round((16*8^n - 63*n - 16)/126).
%F A178827 a(n) = a(n-2) + (8^(n-1) - 1)/7, n > 2.
%F A178827 a(n) = 9*a(n-1) - 7*a(n-2) - 9*a(n-3) + 8*a(n-4), n > 4.
%F A178827 G.f.: x^2/((1+x)*(1-8*x)*(1-x)^2).
%F A178827 7*a(n) = (32*8^n - 126*n - 81 + 49*(-1)^n)/252. - _Bruno Berselli_, Jan 19 2011
%F A178827 a(n) = (floor(8^(n+1)/63) - floor((n+1)/2))/7. - _Seiichi Manyama_, Dec 22 2023
%e A178827 a(3) = (1/7)*(floor(8/9) + floor(64/9) + floor(512/9)) = (1/7)*(0 + 7 + 56) = (1/7)*63 = 9.
%p A178827 A178827 := proc(n) add( floor(8^i/9)/7,i=0..n) ; end proc:
%t A178827 Rest[CoefficientList[Series[x^2/((1+x)*(1-8*x)*(1-x)^2), {x,0,30}],x]] (* _G. C. Greubel_, Jan 22 2019 *)
%o A178827 (Magma) [ &+[Floor(8^k/9)/7: k in [1..n]]: n in [1..25] ]; // _Bruno Berselli_, Apr 28 2011
%o A178827 (Decimal BASIC)
%o A178827 FOR n=1 TO 1000
%o A178827 PRINT n; (32*8^n-126*n-81+49*(-1)^n)/1764
%o A178827 NEXT n
%o A178827 END ! _Bruno Berselli_, Apr 28 2011
%o A178827 (PARI) my(x='x+O('x^30)); concat([0], Vec(x^2/((1+x)*(1-8*x)*(1-x)^2))) \\ _G. C. Greubel_, Jan 22 2019
%o A178827 (Sage) a=(x^2/((1+x)*(1-8*x)*(1-x)^2)).series(x, 30).coefficients(x, sparse=False); a[1:] # _G. C. Greubel_, Jan 22 2019
%o A178827 (GAP) a:=[0,1,9,74];; for n in [5..30] do a[n]:=9*a[n-1]-7*a[n-2]-9*a[n-3] +8*a[n-4]; od; a; # _G. C. Greubel_, Jan 22 2019
%Y A178827 Column k=8 of A368296.
%Y A178827 Cf. A033118.
%K A178827 nonn,less
%O A178827 1,3
%A A178827 _Mircea Merca_, Dec 27 2010