Search: id:A015222
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%I A015222
%S A015222 14,30,140,204,506,650,1240,1496,2470,2870,4324,4900,6930,7714,10416,
%T A015222 11440,14910,16206,20540,22140,27434,29370,35720,38024,45526,48230,
%U A015222 56980,60116,70210,73810,85344,89440,102510,107134,121836,127020
%N A015222 Even square pyramidal numbers.
%C A015222 Square pyramidal numbers k (k + 1) (2 k + 1)/6 are even if and only when 
               k is congruent to 0 or 3 mod 4. [From Artur Jasinski (grafix(AT)csl.pl), 
               Oct 22 2008]
%F A015222 Even numbers of form n(n+1)(2n+1)/6
%F A015222 Contribution from Artur Jasinski (grafix(AT)csl.pl), Oct 22 2008: (Start)
%F A015222 (2 k + 1)/(k + 2)*Binomial[k + 2, 5] if k congruent to 0 or 3 mod 4
%F A015222 k (k + 1) (2 k + 1)/6 if k congruent to 0 or 3 mod 4
%F A015222 (End)
%t A015222 Select[ Table[ n(n+1)(2n+1)/6, {n, 100} ], EvenQ ]
%t A015222 a = {}; j = 1; w = k (k + 1) (2 k + 1)/6; Do[If[Mod[k, 4] == 0, AppendTo[a, 
               w], If[Mod[k, 4] == 3, AppendTo[a, w]]], {k, 1, 100}]; a [From Artur 
               Jasinski (grafix(AT)csl.pl), Oct 22 2008]
%Y A015222 Sequence in context: A104776 A101960 A075208 this_sequence A054103 A161454 
               A156203
%Y A015222 Adjacent sequences: A015219 A015220 A015221 this_sequence A015223 A015224 
               A015225
%K A015222 nonn,easy
%O A015222 1,1
%A A015222 Mohammad K. Azarian (ma3(AT)evansville.edu)
%E A015222 More terms from Erich Friedman (erich.friedman(AT)stetson.edu).

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