This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A244911 #25 Nov 10 2024 02:22:07 %S A244911 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, %T A244911 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, %U A244911 1,10,25,43,61,76,85,85,73,46,1,1,11,28,49,71,91,106,113,109,91 %N A244911 Table read by antidiagonals: T(n,k) = n*k + T(n-1,k) for n >=1, T(0,k) = 1. %C A244911 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. %C A244911 It seems that column C(k) = centered k-gonal numbers, and row R(n) = A000217(n)*k + 1. %C A244911 The triangle under the main diagonal is A121722. %C A244911 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 %H A244911 Kival Ngaokrajang, <a href="/A244911/a244911.pdf">Illustration for n = 0..3, k = 1..4</a> %F A244911 T(n,k) = n*k + T(n-1,k) for n >=1, T(0,k) = 1. %e A244911 Table begins: %e A244911 C0 C1 C2 C3 C4 C5 %e A244911 n/k 0 1 2 3 4 5 ... %e A244911 R0 0 1 1 1 1 1 1 ... %e A244911 R1 1 1 2 3 4 5 6 ... %e A244911 R2 2 1 4 7 10 13 16 ... %e A244911 R3 3 1 7 13 19 25 31 ... %e A244911 R4 4 1 11 21 31 41 51 ... %e A244911 R5 5 1 16 31 46 61 76 ... %e A244911 R6 6 1 22 43 64 85 106 ... %e A244911 R7 7 1 29 57 85 113 141 ... %e A244911 R8 8 1 37 73 109 145 181 ... %e A244911 R9 9 1 46 91 136 181 226 ... %e A244911 ... ... ... ... ... ... ... ... %e A244911 C1 = A000124, C2 = A002061, C3 = A005448, C4 = A001844, C5 = A005891, C6 = A003215, C7 = A069099, C8 = A016754, C9 = A060544, C10 = A062786, C11 = A069125, C12 = A003154. %e A244911 R1 = A000027, R2 = A016777, R3 = A016921, R4 = A017281, R5 = 15*k + 1, R6 = A215146, R7 = A161714. %o A244911 (Small Basic) %o A244911 For k = 0 to 50 %o A244911 a[0][k] = 1 %o A244911 For n = 1 to 50 %o A244911 a[n][k] = n*k + a[n-1][k] %o A244911 EndFor %o A244911 Endfor %o A244911 '================================== %o A244911 For t = 1 to 20 %o A244911 d = 1 %o A244911 For nn = 0 To t-1 %o A244911 kk = t- d %o A244911 TextWindow.Write(a[nn][kk]+", ") %o A244911 d = d + 1 %o A244911 EndFor %o A244911 Endfor %Y A244911 Cf. A000217, A121722, A000124, A002061, A005448, A001844, A005891, A003215, A069099, A016754, A060544, A062786, A069125, A003154, A000027, A016777, A016921, A017281, A215146, A161714. %K A244911 nonn,tabl %O A244911 0,5 %A A244911 _Kival Ngaokrajang_, Jul 07 2014