%I A109678
%S A109678 1,5,14,30,55,91,140,204,285,385,506,650,819,1015,1240,1496,1785,2109,
%T A109678 2470,2870,3311,3795,4324,4900,5525,6201,6930,7714,8555,9455,10416,
%U A109678 11440,12529,13685,14910,16206,17575,19019,20540,22140,23821,25585
%N A109678 Sequence and first differences include all square numbers exactly once.
%C A109678 This sequence diverges from A000330 as 4900 (which is 70^2) appears in 
               the sequence itself - thus won't be added to any a(n).
%F A109678 a(n)=a(n-1)+n^2 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Oct 09 2009]
%e A109678 Superpose sequence and first differences:
%e A109678 1 5 14 30 55 91 140 204 285 385 506 650 819 1015
%e A109678 .4.9..16..25..36..49...64...81...100...121...144...169...196
%e A109678 All square numbers appear once and only once, either in the sequence 
               itself or in the first differences.
%e A109678 For n=2, a(2)=1+4=5; n=3, a(3)=5+9=14; n=4, a(4)=14+16=30 [From Vincenzo 
               Librandi (vincenzo.librandi(AT)tin.it), Oct 09 2009]
%p A109678 seq(sum ((k+1)^2, k=0..n), n=0..41); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Apr 10 2007
%t A109678 s = 1; lst = {s}; Do[s += n^2; AppendTo[lst, s], {n, 2, 42, 1}]; lst 
               [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 12 2009]
%Y A109678 Sequence in context: A136135 A096893 A074784 this_sequence A000330 A166068 
               A070129
%Y A109678 Adjacent sequences: A109675 A109676 A109677 this_sequence A109679 A109680 
               A109681
%K A109678 base,easy,nonn
%O A109678 1,2
%A A109678 Eric Angelini (eric.angelini(AT)kntv.be), Aug 30 2005