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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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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Quasipolynomial of order 2. [Charles R Greathouse IV, Dec 07 2011]
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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: a(2n)= ( 4*n^3 +6*n^2 +8*n +3 )/3, odd: a(2n-1)= ( 4*n^3 +2*n )/3. [Frank Ellermann (hmdmhdfmhdjmzdtjmzdtzktdkztdjz(AT)gmail.com)]
a(n) = SUM(A109613(k)*A109613(n-k): 0<=k<=n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 05 2009]
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PROG
| (PARI) a(n)=if(n%2, 4*n^3+2*n, 4*n^3+6*n^2+8*n+3)/3 \\ Charles R Greathouse IV, Dec 07 2011
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CROSSREFS
| The bisections of the first differences of {a(n)} give A001844 (the centered triangular numbers n^2+(n-1)^2).
Sequence in context: A180804 A122264 A079824 * A177747 A175879 A102371
Adjacent sequences: A059326 A059327 A059328 * A059330 A059331 A059332
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KEYWORD
| nonn,easy
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AUTHOR
| John W. Layman (layman(AT)math.vt.edu), Jan 26 2001
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