OFFSET
1,5
REFERENCES
E. Lucas, Théorie des Nombres, Albert Blanchard, Paris, 1958,tome1, p.88
FORMULA
T(n, k) = C(n, k) - C(n, k-4). - Ralf Stephan, Jan 09 2005
T(2n,n) = A026029(n). - Philippe Deléham, Mar 12 2013
T(2n-1,n) = A026016(n), n>0. - Philippe Deléham, Mar 12 2013
EXAMPLE
From Philippe Deléham, Mar 12 2013: (Start)
Triangle begins:
1
1, 1
1, 2, 1
1, 3, 3, 1
1, 4, 6, 4
1, 5, 10, 10, 4
1, 6, 15, 20, 14
1, 7, 21, 35, 34, 14
1, 8, 28, 56, 69, 48
1, 9, 36, 84, 125, 117, 48
1, 10, 45, 120, 209, 242, 165
1, 11, 55, 165, 329, 451, 407, 165
Pentagon arithmetic of Delannoy (in E. Lucas):
1, 1, 1, 1, 0
1, 2, 3, 4, 4, 0
1, 3, 6, 10, 14, 14, 0
1, 4, 10, 20, 34, 48, 48, 0
1, 5, 15, 35, 69, 117, 165, 165,
1, 6, 21, 56, 125, 242, 407, 572,
1, 7, 28, 84, 209, 451, 858, 1430 (End)
PROG
(PARI) {T(n, k) = if( 2*k < n+4, binomial( n, k) - binomial( n, k-4), 0)} /* Michael Somos, Jan 08 2012 */
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
STATUS
approved