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A001249
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Squares of tetrahedral numbers: binomial(n+3,n)^2.
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12
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1, 16, 100, 400, 1225, 3136, 7056, 14400, 27225, 48400, 81796, 132496, 207025, 313600, 462400, 665856, 938961, 1299600, 1768900, 2371600, 3136441, 4096576, 5290000, 6760000, 8555625, 10732176, 13351716, 16483600, 20205025, 24601600, 29767936, 35808256
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OFFSET
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0,2
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COMMENTS
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Total area of all square and rectangular regions from an n X n grid. e.g. n=3, there are 9 individual squares, 4 2 X 2's and 1 3 X 3, total area 9+16+9=34. The rectangular regions include 6 2 X 1's, 6 1 X 2's, 3 3 X 1's, 3 1 X 3's, 2 3 X 2's and 2 3 X 2's, total area 12+12+9+9+12+12=66, hence a(3)=34+66=100 - Jon Perry, Jul 29 2003
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LINKS
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T. D. Noe, Table of n, a(n) for n = 0..1000
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FORMULA
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a(n)=(A000292(n+1))^2. O.g.f.: x(1+x)(x^2+8x+1)/(1-x)^7. [From R. J. Mathar, Aug 19 2008]
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MAPLE
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[seq(binomial(n+3, n)^2, n=0..50)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 17 2006
a:=n->sum(sum(binomial(j, 2)*binomial(k, 2), j=0..n), k=0..n): seq(a(n), n=2..28); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 02 2007
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MATHEMATICA
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Table[Binomial[n + 3, 3]^2, {n, 0, 100}] (* T. D. Noe, Jun 26 2012 *)
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CROSSREFS
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Cf. A000292.
Cf. A033455.
Third column of triangle A008459.
Sequence in context: A045784 A016958 A108677 * A014796 A052206 A169721
Adjacent sequences: A001246 A001247 A001248 * A001250 A001251 A001252
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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