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Search: id:A015222
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| A015222 |
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Even square pyramidal numbers. |
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+0
1
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| 14, 30, 140, 204, 506, 650, 1240, 1496, 2470, 2870, 4324, 4900, 6930, 7714, 10416, 11440, 14910, 16206, 20540, 22140, 27434, 29370, 35720, 38024, 45526, 48230, 56980, 60116, 70210, 73810, 85344, 89440, 102510, 107134, 121836, 127020
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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]
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FORMULA
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Even numbers of form n(n+1)(2n+1)/6
Contribution from Artur Jasinski (grafix(AT)csl.pl), Oct 22 2008: (Start)
(2 k + 1)/(k + 2)*Binomial[k + 2, 5] if k congruent to 0 or 3 mod 4
k (k + 1) (2 k + 1)/6 if k congruent to 0 or 3 mod 4
(End)
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MATHEMATICA
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Select[ Table[ n(n+1)(2n+1)/6, {n, 100} ], EvenQ ]
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]
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CROSSREFS
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Sequence in context: A104776 A101960 A075208 this_sequence A054103 A161454 A156203
Adjacent sequences: A015219 A015220 A015221 this_sequence A015223 A015224 A015225
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KEYWORD
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nonn,easy
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AUTHOR
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Mohammad K. Azarian (ma3(AT)evansville.edu)
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EXTENSIONS
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More terms from Erich Friedman (erich.friedman(AT)stetson.edu).
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