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 A173154 #27 Oct 12 2024 02:35:43
%S A173154 1,4,10,19,33,52,78,111,153,204,266,339,425,524,638,767,913,1076,1258,
%T A173154 1459,1681,1924,2190,2479,2793,3132,3498,3891,4313,4764,5246,5759,
%U A173154 6305,6884,7498,8147,8833,9556,10318,11119,11961,12844,13770,14739,15753,16812,17918,19071,20273,21524
%N A173154 a(n) = n^3/6 + 3*n^2/4 + 7*n/3 + 7/8 + (-1)^n/8.
%C A173154 Generated by reading the table shown in A172002 down the diagonal starting at 1.
%C A173154 The inverse binomial transform yields 1, 3, 3, 0, 2, -4, 8, -16, 32, -64, 128, -256, 512, -1024, ... with a pattern of powers of 2.
%H A173154 Vincenzo Librandi, <a href="/A173154/b173154.txt">Table of n, a(n) for n = 0..10000</a>
%H A173154 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-2,3,-1).
%F A173154 G.f.: ( 1 + x - x^3 + x^4 ) / ( (1+x)*(x-1)^4 ).
%F A173154 a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - a(n-5).
%F A173154 a(n+4) - a(n) = 4*A152948(n+5) = 4*A089071(n+5).
%F A173154 First differences: a(n+1) - a(n) = A061925(n+2).
%F A173154 Second differences: a(n+2) - 2*a(n+1) + a(n) = n + 5/2 + (-1)^n/2 = 3, 3, 5, 5, 7, 7, 9, 9, ... , duplicated A144396.
%t A173154 Table[n^3/6+(3n^2)/4+(7n)/3+7/8+(-1)^n/8,{n,0,50}] (* or *) LinearRecurrence[{3,-2,-2,3,-1},{1,4,10,19,33},50] (* _Harvey P. Dale_, Jan 04 2012 *)
%o A173154 (Magma) [n^3/6 + 3*n^2/4 + 7*n/3 + 7/8 + (-1)^n/8: n in [0..50]]; // _Vincenzo Librandi_, Aug 05 2011
%K A173154 nonn,easy
%O A173154 0,2
%A A173154 _Paul Curtz_, Feb 11 2010