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Search: id:A134507
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| A134507 |
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The number of rectangles in a pyramid built with squares. The squares counted in A131177 are excluded. |
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+0
2
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| 0, 4, 19, 57, 134, 269, 486, 813, 1281, 1926, 2788, 3910, 5340, 7130, 9335, 12015, 15234, 19059, 23562, 28819, 34909, 41916, 49928, 59036, 69336, 80928, 93915, 108405, 124510, 142345, 162030, 183689, 207449, 233442, 261804, 292674, 326196
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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At the first step, the pyramid contains only one unitary square.At each step of rank n we add a row of 2*n-1 squares below the previous pyramid. The sequence is the number of rectangles of any size which can be seen in this pyramid oh height n
.__..........___.
|..|.........|..|
|__|......___|__|__
..........|..|..|..|
..0.......|__|__|__| 3 rectangles 2X1, 1 rectangle 3X1
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FORMULA
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For n == 0 mod 3, c(n) = n*((3*n^3)+(5*n^2)-(3^n)-3)/18; for n == 1 mod 3, c(n) = (n-1)*(3*(n^3]+8*(n^2)+5*n+2)/18; for n == 2 mod 3, c(n) = (3*(n^4)+5*(n^3)-3*(n^2)-3*n+2)/18
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PROGRAM
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(PARI) {a(n) = (3*n^4 + 5*n^3 - 3*n^2 - 3*n + 2) \ 18} /* Michael Somos Feb 17 2008 */
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CROSSREFS
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Cf. A131177.
Sequence in context: A122681 A020496 A108484 this_sequence A098813 A055485 A000306
Adjacent sequences: A134504 A134505 A134506 this_sequence A134508 A134509 A134510
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KEYWORD
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easy,nonn
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AUTHOR
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Philippe Lallouet (philip.lallouet(AT)orange.fr), Jan 19 2008
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