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A139601 Square array T(n,k) = (n+1)*(k-1)*k/2+k, of polygonal numbers, read by antidiagonals upwards. 14
0, 0, 1, 0, 1, 3, 0, 1, 4, 6, 0, 1, 5, 9, 10, 0, 1, 6, 12, 16, 15, 0, 1, 7, 15, 22, 25, 21, 0, 1, 8, 18, 28, 35, 36, 28, 0, 1, 9, 21, 34, 45, 51, 49, 36, 0, 1, 10, 24, 40, 55, 66, 70, 64, 45, 0, 1, 11, 27, 46, 65, 81, 91, 92, 81, 55, 0, 1, 12, 30, 52, 75, 96, 112, 120, 117, 100, 66 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

A general formula for polygonal numbers is P(n,k) = (n-2)(k-1)k/2 + k, where P(n,k) is the k-th n-gonal number. - Omar E. Pol, Dec 21 2008

LINKS

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Peter Luschny, Figurate number — a very short introduction. With plots from Stefan Friedrich Birkner.

Omar E. Pol, Polygonal numbers, An alternative illustration of initial terms.

FORMULA

T(n,k) = A086270(n,k), k>0. - R. J. Mathar, Aug 06 2008

T(n,k) = (n+1)*(k-1)*k/2+k, n>=0, k>=0. - Omar E. Pol, Jan 07 2009

EXAMPLE

The square array of polygonal numbers begins:

========================================================

Triangulars .. A000217: 0, 1,  3,  6, 10,  15,  21,  28,

Squares ...... A000290: 0, 1,  4,  9, 16,  25,  36,  49,

Pentagonals .. A000326: 0, 1,  5, 12, 22,  35,  51,  70,

Hexagonals ... A000384: 0, 1,  6, 15, 28,  45,  66,  91,

Heptagonals .. A000566: 0, 1,  7, 18, 34,  55,  81, 112,

Octagonals ... A000567: 0, 1,  8, 21, 40,  65,  96, 133,

9-gonals ..... A001106: 0, 1,  9, 24, 46,  75, 111, 154,

10-gonals .... A001107: 0, 1, 10, 27, 52,  85, 126, 175,

11-gonals .... A051682: 0, 1, 11, 30, 58,  95, 141, 196,

12-gonals .... A051624: 0, 1, 12, 33, 64, 105, 156, 217,

And so on ..............................................

========================================================

MATHEMATICA

T[n_, k_] := (n + 1)*(k - 1)*k/2 + k; Table[ T[n - k, k], {n, 0, 11}, {k, 0, n}] // Flatten [Robert G. Wilson v, Jul 12 2009]

CROSSREFS

Sequences of m-gonal numbers: A000217 (m=3), A000290 (m=4), A000326 (m=5), A000384 (m=6), A000566 (m=7), A000567 (m=8), A001106 (m=9), A001107 (m=10), A051682 (m=11), A051624 (m=12), A051865 (m=13), A051866 (m=14), A051867 (m=15), A051868 (m=16), A051869 (m=17), A051870 (m=18), A051871 (m=19), A051872 (m=20), A051873 (m=21), A051874 (m=22), A051875 (m=23), A051876 (m=24), A255184 (m=25), A255185 (m=26), A255186 (m=27), A161935 (m=28), A255187 (m=29), A254474 (m=30).

Cf. A000007, A000012, A000027, A008585, A016957, A017329, A139606, A139607, A139608, A139609, A139610, A139611, A139612, A139613, A139614, A139615, A139616, A057145, A086271, A139600.

Cf. A086270, A139617, A139618, A139619, A139620.

Sequence in context: A250104 A220421 A106683 * A213191 A079520 A229001

Adjacent sequences:  A139598 A139599 A139600 * A139602 A139603 A139604

KEYWORD

nonn,tabl,easy

AUTHOR

Omar E. Pol, Apr 27 2008

STATUS

approved

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Last modified October 18 23:39 EDT 2019. Contains 328211 sequences. (Running on oeis4.)