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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-Fran├žois 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.)