OFFSET
1,2
COMMENTS
This triangle is motivated by sequence A256885 by Wesley Ivan Hurt, which is the sequence of row sums for n >= 1.
Row n ends in a 0 if n is prime; otherwise it ends in 1.
The alternating row sums give 1, seven times 2, six times 3, six times 4, four times 5, twice 6, ..., and the multiplicity sequence 1, 7, 6, 6, 4, 2, ... is given in A257233.
LINKS
Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened
FORMULA
T(n, k) = n - (k-1) - [isprime(k)], with [isprime(k)] = A010051(k), for 1 <= k <= n.
O.g.f. for column k (with leading zeros): x^k/(1-x)^2 if k is nonprime, otherwise x^(k+1)/(1-x)^2.
T(n+1,k) = T(n,k) + 1, 1 <= k <= n, T(n+1,n+1) = 1 - A010051(n+1). - Reinhard Zumkeller, Apr 21 2015
EXAMPLE
The triangle T(n, k) begins:
n\k 1 2 3 4 5 6 7 8 9 10 11 ...
1: 1
2: 2 0
3: 3 1 0
4: 4 2 1 1
5: 5 3 2 2 0
6: 6 4 3 3 1 1
7: 7 5 4 4 2 2 0
8: 8 6 5 5 3 3 1 1
9: 9 7 6 6 4 4 2 2 1
10: 10 8 7 7 5 5 3 3 2 1
11: 11 9 8 8 6 6 4 4 3 2 0
...
MATHEMATICA
Table[n - (k - 1) - Boole[PrimeQ@ k], {n, 11}, {k, n}] // Flatten (* Michael De Vlieger, Apr 19 2015 *)
PROG
(Haskell)
a257232 n k = a257232_tabl !! (n-1) !! (k-1)
a257232_row n = a257232_tabl !! (n-1)
a257232_tabl = iterate
(\xs@(x:_) -> map (+ 1) xs ++ [1 - a010051 (x + 1)]) [1]
-- Reinhard Zumkeller, Apr 21 2015
CROSSREFS
KEYWORD
AUTHOR
Wolfdieter Lang, Apr 19 2015
STATUS
approved