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 A139601 Square array T(n,k) = (n+1)*(k-1)*k/2+k, of polygonal numbers, read by antidiagonals upwards. 15
 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 April 21 14:32 EDT 2021. Contains 343154 sequences. (Running on oeis4.)