login
A073152
Triangle of numbers relating two simple context-free grammars (A052709 and A052705).
1
1, 1, 2, 3, 4, 7, 9, 12, 15, 24, 31, 40, 49, 58, 89, 113, 144, 171, 198, 229, 342, 431, 544, 637, 718, 811, 924, 1355, 1697, 2128, 2467, 2746, 3025, 3364, 3795, 5492, 6847, 8544, 9837, 10854, 11815, 12832, 14125, 15822, 22669, 28161
OFFSET
0,3
COMMENTS
Sequence A052705 is the convolution of A052709.
LINKS
D. Merlini, D. G. Rogers, R. Sprugnoli and M. C. Verri, On some alternative characterizations of Riordan arrays, Canad. J. Math. 49 (1997) 301
FORMULA
Triangle {a(n, k), n >= 0, 0<=k<=n} defined by: a(0, 0)=1, a(n, 0)=A052709(n+1), a(n, n)=A052705(n+2), a(n, 0)=a(n-1, n-1) + a(n-2, n-2), a(n, k)=sum{j=0..k} A052709(j+1) * a(n-j, 0).
EXAMPLE
a(5,0)=a(3,3)+a(4,4)=24+89=113. a(5,3)=1*a(5,0)+1*a(4,0)+3*a(3,0)+9*a(2,0)=1*113+1*31+3*9+9*3=198. Rows: {1}; {1,2}; {3,4,7}; {9,12,15,24}; {31,40,49,58,89}; {113,144,171,198,229,342}; {431,544,637,718,811,924,1355}; {1697,2128,2467,2746,3025,3364,3795,5492}
CROSSREFS
Sequence in context: A270839 A117450 A132381 * A325092 A375601 A247186
KEYWORD
easy,nonn,tabl
AUTHOR
Paul D. Hanna, Jul 29 2002
STATUS
approved