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 A086271 Rectangular array T(n,k) of polygonal numbers, by diagonals. 9
 1, 1, 3, 1, 4, 6, 1, 5, 9, 10, 1, 6, 12, 16, 15, 1, 7, 15, 22, 25, 21, 1, 8, 18, 28, 35, 36, 28, 1, 9, 21, 34, 45, 51, 49, 36, 1, 10, 24, 40, 55, 66, 70, 64, 45, 1, 11, 27, 46, 65, 81, 91, 92, 81, 55, 1, 12, 30, 52, 75, 96, 112, 120, 117, 100, 66, 1, 13, 33, 58, 85, 111, 133, 148, 153, 145, 121, 78 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The transpose of A086270; diagonal sums 1,4,11,25,50,... are the numbers A006522(n) for n>=3. Transpose of the array in A086270; diagonal sums 1,4,11,25,50,... are the numbers A006522(n) for n>=3. LINKS G. C. Greubel, Table of n, a(n) for the first 50 diagonals, flattened Clark Kimberling and John E. Brown, Partial Complements and Transposable Dispersions, J. Integer Seqs., Vol. 7, 2004. FORMULA T(n, k) = k*C(n, 2)+n. EXAMPLE Columns 1,2,3 are the triangular, square and pentagonal numbers. Northwest corner: 1  1   1  1  1 ... 3  4   5  6  7 ... 6  9  12 15 18 ... 10 16 22 28 34 ... 15 25 35 45 55 ... ... MATHEMATICA T[n_, k_] := PolygonalNumber[k+2, n]; Table[T[n-k+1, k], {n, 1, 12}, {k, n, 1, -1}] // Flatten (* Jean-François Alcover, Sep 04 2016 *) CROSSREFS Cf. A086270, A086272, A086273. Sequence in context: A307394 A194540 A193043 * A080851 A209518 A108285 Adjacent sequences:  A086268 A086269 A086270 * A086272 A086273 A086274 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Jul 14 2003 STATUS approved

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Last modified May 10 19:32 EDT 2021. Contains 343780 sequences. (Running on oeis4.)