OFFSET
1,2
COMMENTS
Row sums are 0, 1, 6, 27, 88, 200, ... with g.f. -x*(1 + 4*x + 16*x^2 + 37*x^3 + 39*x^4 + 54*x^5 + 39*x^6 + 17*x^7 + 8*x^8 + x^9) / ( (1 + x + x^2)^3*(x-1)^5 ). - R. J. Mathar, Aug 10 2017
LINKS
Reinhard Zumkeller, Rows n = 1..100, flattened
Gary E. Stevens, A Connell-Like Sequence, J. Integer Sequences, 1 (1998), #98.1.4.
FORMULA
a(n) = q(n)*n - q(n)*floor(q(n)*(q(n)+1)/6) with q(n) = ceiling((1/2)*(-1 + sqrt(1+8*(n)))).
EXAMPLE
Triangle begins
1;
2, 4;
6, 9, 12;
16, 20, 24, 28;
30, 35, 40, 45, 50;
54, 60, 66, 72, 78, 84;
91, 98, 105, 112, 119, 126, 133; ...
MAPLE
A033291 := proc(n, k)
A192735(n)+(k-1)*n ;
end proc:
seq(seq(A033291(n, k), k=1..n), n=1..10) ; # R. J. Mathar, Aug 10 2017
MATHEMATICA
Flatten[ Table[ n*(Floor[ (n-1)^2/3] + k), {n, 1, 12}, {k, 1, n}]] (* Jean-François Alcover, Sep 30 2011 *)
PROG
(Haskell)
a033291 n k = a033291_tabl !! (n-1) !! (k-1)
a033291_row n = a033291_tabl !! (n-1)
a033291_tabl = f 1 [1..] where
f k xs = ys : f (k+1) (dropWhile (<= last ys) xs) where
ys = take k $ filter ((== 0) . (`mod` k)) xs
a192735 n = head $ a033291_tabl !! (n-1)
a192736 n = last $ a033291_tabl !! (n-1)
-- Reinhard Zumkeller, Jan 18 2012, Jul 08 2011
(PARI) a(n)=my(q=(sqrtint(8*n-7)+1)\2); q*n-q*(q+1)\6*q \\ Charles R Greathouse IV, Jan 06 2016
CROSSREFS
KEYWORD
AUTHOR
EXTENSIONS
Corrected and formula added by Johannes W. Meijer, Oct 07 2010
STATUS
approved