OFFSET
1,8
COMMENTS
The rows of the Pascal triangle are here found as square root parabolas like in the plots at www.divisorplot.com. Central binomial coefficients are found at the square root boundary.
A156348 * A000010 = A156834: (1, 2, 3, 5, 5, 12, 7, 17, 19, 30, 11, ...). - Gary W. Adamson, Feb 16 2009
Row sums give A157019.
LINKS
Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened
el Houcein el Abdalaoui, Mohamed Dahmoune and Djelloul Ziadi, On the transition reduction problem for finite automata, arXiv preprint arXiv:1301.3751 [cs.FL], 2013. - From N. J. A. Sloane, Feb 12 2013
Jeff Ventrella, Divisor Plot
EXAMPLE
Table begins:
1
1 1
1 0 1
1 2 0 1
1 0 0 0 1
1 3 3 0 0 1
1 0 0 0 0 0 1
1 4 0 4 0 0 0 1
1 0 6 0 0 0 0 0 1
1 5 0 0 5 0 0 0 0 1
1 0 0 0 0 0 0 0 0 0 1
1 6 10 10 0 6 0 0 0 0 0 1
1 0 0 0 0 0 0 0 0 0 0 0 1
1 7 0 0 0 0 7 0 0 0 0 0 0 1
1 0 15 0 15 0 0 0 0 0 0 0 0 0 1
1 8 0 20 0 0 0 8 0 0 0 0 0 0 0 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 9 21 0 0 21 0 0 9 0 0 0 0 0 0 0 0 1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
1 10 0 35 35 0 0 0 0 10 0 0 0 0 0 0 0 0 0 1
MAPLE
A156348 := proc(n, k)
if k < 1 or k > n then
return 0 ;
elif n mod k = 0 then
binomial(n/k-2+k, k-1) ;
else
0 ;
end if;
end proc: # R. J. Mathar, Mar 03 2013
MATHEMATICA
T[n_, k_] := Which[k < 1 || k > n, 0, Mod[n, k] == 0, Binomial[n/k - 2 + k, k - 1], True, 0];
Table[T[n, k], {n, 1, 14}, {k, 1, n}] // Flatten (* Jean-François Alcover, Nov 16 2017 *)
PROG
(Haskell) Following Mathar's Maple program.
a156348 n k = a156348_tabl !! (n-1) !! (k-1)
a156348_tabl = map a156348_row [1..]
a156348_row n = map (f n) [1..n] where
f n k = if r == 0 then a007318 (n' - 2 + k) (k - 1) else 0
where (n', r) = divMod n k
-- Reinhard Zumkeller, Jan 31 2014
CROSSREFS
AUTHOR
Mats Granvik, Feb 08 2009
STATUS
approved