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A086270
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Rectangular array T(k,n) of polygonal numbers, by antidiagonals.
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13
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1, 3, 1, 6, 4, 1, 10, 9, 5, 1, 15, 16, 12, 6, 1, 21, 25, 22, 15, 7, 1, 28, 36, 35, 28, 18, 8, 1, 36, 49, 51, 45, 34, 21, 9, 1, 45, 64, 70, 66, 55, 40, 24, 10, 1, 55, 81, 92, 91, 81, 65, 46, 27, 11, 1, 66, 100, 117, 120, 112, 96, 75, 52, 30, 12, 1, 78, 121, 145, 153, 148, 133, 111
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The antidiagonal sums 1,4,11,25,50,... are the numbers A006522(n) for n>=3.
This is the accumulation array (Cf. A144112) of A144257 (which is the weight array of A086270). [From Clark Kimberling (ck6(AT)evansville.edu), Sep 16 2008]
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LINKS
| Clark Kimberling and John E. Brown, Partial Complements and Transposable Dispersions, J. Integer Seqs., Vol. 7, 2004.
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FORMULA
| T(n,k)=n*C(k,2)+k.
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EXAMPLE
| First 6 rows:
1...3....6...10...15... (A000217, triangular numbers)
1...4....9...16...25... (A000290, squares)
1...5...12...22...35... (A000326, pentagonal numbers)
1...6...15...28...45... (A000384, hexagonal numbers)
1...7...18...34...55... (A000566, heptagonal numbers)
1...8...21...40...65... (A000567, octagonal numbers)
The array formed by the complements: A183225.
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MATHEMATICA
| t[n_, k_] := n*Binomial[k, 2] + k; Table[ t[k, n - k + 1], {n, 12}, {k, n}] // Flatten
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CROSSREFS
| Cf. A086271, A086272, A086273.
Cf. A144257. [From Clark Kimberling (ck6(AT)evansville.edu), Sep 16 2008]
Sequence in context: A201904 A133110 A185915 * A104712 A122177 A108286
Adjacent sequences: A086267 A086268 A086269 * A086271 A086272 A086273
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KEYWORD
| nonn,tabl
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu), Jul 14 2003
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EXTENSIONS
| Extended by Clark Kimberling (ck6(AT)evansville.edu), Jan 01 2011
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