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Search: id:A059329
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| A059329 |
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Number of 3 X 3 matrices, with elements from {0,...,n}, having the property that the middle element of each of the eight 3-element horizontal, vertical, and diagonal lines equals the average of the two end elements. |
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+0
1
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| 1, 2, 7, 12, 25, 38, 63, 88, 129, 170, 231, 292, 377, 462, 575, 688, 833, 978, 1159, 1340, 1561, 1782, 2047, 2312, 2625, 2938, 3303, 3668, 4089, 4510, 4991, 5472, 6017, 6562, 7175, 7788, 8473, 9158, 9919, 10680, 11521, 12362, 13287, 14212
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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even: a(2n)= ( 4*n^3 +6*n^2 +8*n +3 )/3, odd: a(2n-1)= ( 4*n^3 +2*n )/3, (frank.ellermann(AT)t-online.de).
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CROSSREFS
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The bisections of the first differences of {a(n)} give A001844 (the centered triangular numbers n^2+(n-1)^2).
Adjacent sequences: A059326 A059327 A059328 this_sequence A059330 A059331 A059332
Sequence in context: A135541 A122264 A079824 this_sequence A102371 A007230 A059053
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KEYWORD
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nonn
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Jan 26 2001
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