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
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 ...
... ... ... ... ... ... ... ...
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
KEYWORD
nonn,tabl
AUTHOR
Kival Ngaokrajang, Jul 07 2014
STATUS
approved