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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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Sequence A052705 is the convolution of A052709.

LINKS

Table of n, a(n) for n=0..45.

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

Cf. A052709, A052705.

Sequence in context: A270839 A117450 A132381 * A325092 A247186 A051061

Adjacent sequences: A073149 A073150 A073151 * A073153 A073154 A073155

KEYWORD

easy,nonn,tabl

AUTHOR

Paul D. Hanna, Jul 29 2002

STATUS

approved

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Last modified February 7 17:21 EST 2023. Contains 360128 sequences. (Running on oeis4.)