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A015222
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Even square pyramidal numbers.
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0
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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; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).
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FORMULA
| Even entries in A000330.
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)
G.f. 2*x*(7+x*(8+x*(34+x*(8+7*x)))))/ ((-1+x)^4*(1+x)^3) [From Harvey P. Dale, May 05 2011]
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MATHEMATICA
| Select[ Table[ n(n+1)(2n+1)/6, {n, 100} ], EvenQ ]
Select[Rest[CoefficientList[Series[(x(x+1))/(x-1)^4, {x, 0, 80}], x]], EvenQ] (* From Harvey P. Dale, May 05 2011 *)
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CROSSREFS
| Cf. A000330.
Sequence in context: A104776 A101960 A075208 * A054103 A161454 A156203
Adjacent sequences: A015219 A015220 A015221 * A015223 A015224 A015225
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KEYWORD
| nonn,easy
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AUTHOR
| Mohammad K. Azarian (ma3(AT)evansville.edu)
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EXTENSIONS
| More terms from Erich Friedman (erich.friedman(AT)stetson.edu).
G.f. adapted to the offset by Bruno Berselli, May 16 2011
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