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 A244911 Table read by antidiagonals: T(n,k) = n*k + T(n-1,k) for n >=1, T(0,k) = 1. 1
 1, 1, 1, 1, 2, 1, 1, 3, 4, 1, 1, 4, 7, 7, 1, 1, 5, 10, 13, 11, 1, 1, 6, 13, 19, 21, 16, 1, 1, 7, 16, 25, 31, 31, 22, 1, 1, 8, 19, 31, 41, 46, 43, 29, 1, 1, 9, 22, 37, 51, 61, 64, 57, 37, 1, 1, 10, 25, 43, 61, 76, 85, 85, 73, 46, 1, 1, 11, 28, 49, 71, 91, 106, 113, 109, 91 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS T(n,k) is the total number of boxes, when we start with 1 center box (n = 0) then expand 1 box on k-arms for each n iteration. See illustration in links. It seems that column C(k) = centered k-gonal numbers, and row R(n) = A000217(n)*k + 1. The triangle under the main diagonal is A121722. Column N (CN) is the Narayana transform (A001263) of (1, N, 0, 0, 0. Example: C2 (1, 3, 7, 13, ...) is the Narayana transform of (1, 2, 0, 0, 0, ...). - Gary W. Adamson, Oct 01 2015 LINKS Table of n, a(n) for n=0..75. Kival Ngaokrajang, Illustration for n = 0..3, k = 1..4 FORMULA T(n,k) = n*k + T(n-1,k) for n >=1, T(0,k) = 1. EXAMPLE Table begins: C0 C1 C2 C3 C4 C5 n/k 0 1 2 3 4 5 ... R0 0 1 1 1 1 1 1 ... R1 1 1 2 3 4 5 6 ... R2 2 1 4 7 10 13 16 ... R3 3 1 7 13 19 25 31 ... R4 4 1 11 21 31 41 51 ... R5 5 1 16 31 46 61 76 ... R6 6 1 22 43 64 85 106 ... R7 7 1 29 57 85 113 141 ... R8 8 1 37 73 109 145 181 ... R9 9 1 46 91 136 181 226 ... ... ... ... ... ... ... ... ... C1 = A000124, C2 = A002061, C3 = A005448, C4 = A001844, C5 = A005891, C6 = A003215, C7 = A069099, C8 = A016754, C9 = A060544, C10 = A062786, C11 = A069125, C12 = A003154. R1 = A000027, R2 = A016777, R3 = A016921, R4 = A017281, R5 = 15*k + 1, R6 = A215146, R7 = A161714. PROG (Small Basic) For k = 0 to 50 a[0][k] = 1 For n = 1 to 50 a[n][k] = n*k + a[n-1][k] EndFor Endfor '================================== For t = 1 to 20 d = 1 For nn = 0 To t-1 kk = t- d TextWindow.Write(a[nn][kk]+", ") d = d + 1 EndFor Endfor CROSSREFS Cf. A000217, A121722, A000124, A002061, A005448, A001844, A005891, A003215, A069099, A016754, A060544, A062786, A069125, A003154, A000027, A016777, A016921, A017281, A215146, A161714. Sequence in context: A113749 A109225 A112564 * A258309 A197957 A089899 Adjacent sequences: A244908 A244909 A244910 * A244912 A244913 A244914 KEYWORD nonn,tabl AUTHOR Kival Ngaokrajang, Jul 07 2014 STATUS approved

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Last modified September 16 19:55 EDT 2024. Contains 375977 sequences. (Running on oeis4.)