OFFSET
1,12
COMMENTS
With sequences constructed of successively larger kxk square matrices (cf. A074279), a(n) will return the distance of n from the top edge of the matrix that n is located in, with 0 standing for the topmost row in that matrix (please see the Example section).
A237451 gives the corresponding column index.
A238013 and A121997 give these same row and column indices, but starting the numbering with index 1. - M. F. Hasler, Feb 17 2014
LINKS
Antti Karttunen, Table of squares with sizes 1x1 .. 30x30, flattened
FORMULA
a(n) = A238013(n)-1. - M. F. Hasler, Feb 16 2014
EXAMPLE
This irregular table begins as:
0;
0,0;
1,1;
0,0,0;
1,1,1;
2,2,2;
0,0,0,0;
1,1,1,1;
2,2,2,2;
3,3,3,3;
0,0,0,0,0;
1,1,1,1,1;
2,2,2,2,2;
3,3,3,3,3;
4,4,4,4,4;
...
PROG
(Python)
from sympy import integer_nthroot
def A237452(n): return (n-1-(k:=(m:=integer_nthroot(3*n, 3)[0])+(6*n>m*(m+1)*((m<<1)+1)))*(k-1)*((k<<1)-1)//6)//k # Chai Wah Wu, Nov 04 2024
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Antti Karttunen, Feb 08 2014
STATUS
approved