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 A037235 #42 Oct 21 2022 18:33:50
%S A037235 0,1,4,13,32,65,116,189,288,417,580,781,1024,1313,1652,2045,2496,3009,
%T A037235 3588,4237,4960,5761,6644,7613,8672,9825,11076,12429,13888,15457,
%U A037235 17140,18941,20864,22913,25092,27405,29856,32449,35188,38077,41120,44321,47684,51213
%N A037235 a(n) = n*(2*n^2 - 3*n + 4)/3.
%C A037235 Row sums of triangle A134249. Also, binomial transform of (1, 3, 6, 4, 0, 0, 0, ...). - _Gary W. Adamson_, Oct 15 2007
%C A037235 Binomial transform of a(n) starts: 0, 1, 6, 28, 112, 400, 1312, 4032, ... . - _Wesley Ivan Hurt_, Oct 21 2014
%C A037235 Number of equivalence classes of n-tuples from the set {1,0,-1} where at the number of nonzero elements is 1,2, or 3 and two n-tuples are equivalent if they are negatives of each other. - _Michael Somos_, Oct 19 2022
%H A037235 Vincenzo Librandi, <a href="/A037235/b037235.txt">Table of n, a(n) for n = 0..1000</a>
%H A037235 T. A. Gulliver, <a href="http://web.archive.org/web/20070218033906/http://www.ece.uvic.ca/~agullive/square.ps">Sequences from Arrays of Integers</a>, Int. Math. Journal, Vol. 1, No. 4, pp. 323-332, 2002.
%H A037235 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A037235 G.f.: x*(1+3*x^2)/(1-x)^4.
%F A037235 a(n) = Sum_{k=0..n-1} (2*k^2 + 1). - _Mike Warburton_, Sep 08 2007
%F A037235 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) with n>3, a(0)=0, a(1)=1, a(2)=4, a(3)=13. - _Yosu Yurramendi_, Sep 03 2013
%F A037235 a(n+1) = a(n) + A058331(n). - _Michael Somos_, Oct 19 2022
%p A037235 A037235:=n->n*(2*n^2-3*n+4)/3: seq(A037235(n), n=0..50); # _Wesley Ivan Hurt_, Oct 21 2014
%t A037235 Table[n (2 n^2 - 3 n + 4)/3, {n, 0, 50}] (* _Wesley Ivan Hurt_, Oct 21 2014 *)
%o A037235 (PARI) A037235(n) = n*(2*n^2-3*n+4)/3 \\ _Michael B. Porter_, Dec 07 2009
%o A037235 (Magma) [n*(2*n^2-3*n+4)/3: n in [0..40]]; // _Vincenzo Librandi_, Jun 15 2011
%o A037235 (R)
%o A037235 a <- c(0, 1, 4, 13)
%o A037235 for(n in (length(a)+1):30) a[n] <- 4*a[n-1] -6*a[n-2] +4*a[n-3] -a[n-4]
%o A037235 a
%o A037235 # _Yosu Yurramendi_, Sep 03 2013
%Y A037235 Cf. A058331, A134249.
%K A037235 nonn,easy
%O A037235 0,3
%A A037235 _N. J. A. Sloane_