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A139601 Square array T(n,k) = (n+1)*(k-1)*k/2+k, of polygonal numbers, read by antidiagonals. 5
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

Table of n, a(n) for n=0..77.

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

Cf. A000217, A000290, A000326, A000384, A000566, A000567, A001106, A001107, A051682, A051624, A051865, A051866, A051867, A051868, A051869, A051870, 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 March 27 22:02 EDT 2017. Contains 284182 sequences.