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Search: id:A086270
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| A086270 |
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Rectangular array T(k,n) of polygonal numbers, by antidiagonals. |
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+0
8
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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; listen)
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OFFSET
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1,2
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COMMENT
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The diagonal sums 1,4,11,25,50,... are the numbers A006522(n) for n>=3.
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
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Clark Kimberling and John E. Brown, Partial Complements and Transposable Dispersions, J. Integer Seqs., Vol. 7, 2004.
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FORMULA
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T(k, n)=kC(n, 2)+n.
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EXAMPLE
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First 3 rows:
(1) triangular numbers: 1 3 6 10 15 ... (A000217)
(2) square numbers: 1 4 9 16 25 ... (A000290)
(3) pentagonal numbers: 1 5 12 22 35 ... (A000326)
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CROSSREFS
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Cf. A086271, A086272, A086273.
Cf. A144257. [From Clark Kimberling (ck6(AT)evansville.edu), Sep 16 2008]
Sequence in context: A070883 A120029 A133110 this_sequence A104712 A122177 A108286
Adjacent sequences: A086267 A086268 A086269 this_sequence A086271 A086272 A086273
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Jul 14 2003
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