A073152 Triangle of numbers relating two simple context-free grammars (A052709 and A052705).

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

Author

Paul D. Hanna, Jul 29 2002

Keywords

• easy
• nonn
• tabl

Comments

Sequence A052705 is the convolution of A052709.

Examples

			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}
		

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

Crossrefs

Cf. A052709, A052705.

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).