OFFSET
0,6
REFERENCES
B. A. Bondarenko, Generalized Pascal Triangles and Pyramids (in Russian), FAN, Tashkent, 1990, ISBN 5-648-00738-8. English translation published by Fibonacci Association, Santa Clara Univ., Santa Clara, CA, 1993; see p. 44.
FORMULA
T(n, m) = T(n-1, m-2) + T(n-1, m-1) + T(n-1, m) - 2*T(n-2, m-2). In words, each entry is the sum of 3 entries above it (i.e., in the previous row) minus twice the entry two rows above it.
EXAMPLE
Triangle begins
. . . 1
. . 1 1 1
. 1 2 1 2 1
1 3 2 3 2 3 1
MAPLE
T := proc(n, m) option remember: if m=0 then RETURN(1) fi: if m=2*n then RETURN(1) fi: if n=1 and m=1 then RETURN(1) fi: if n=2 and m mod 2 = 0 and m >= 0 and m<=2*n then RETURN(1) fi: if n=2 and m mod 2 = 1 and m >= 0 and m<=2*n then RETURN(2) fi: if m>2*n then RETURN(0) fi: if m<0 then RETURN(0) fi: T(n-1, m-2)+T(n-1, m-1)+T(n-1, m)-2*T(n-2, m-2): end:for n from 0 to 10 do for m from 0 to 2*n do printf(`%d, `, T(n, m)) od: od: # James A. Sellers, Feb 24 2001
CROSSREFS
KEYWORD
nonn,easy,tabf
AUTHOR
N. J. A. Sloane, Feb 22 2001
EXTENSIONS
More terms from James A. Sellers, Feb 24 2001
STATUS
approved