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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 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.)