A073151 - OEIS

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A073151

Triangle of numbers {a(n,k), n >= 0, 0<=k<=n} defined by a(0,0)=1, a(n+1,0)=A006319(n)=a(n,0) + Sum a(k,k), k=0..n-1. a(n,m+1)= a(n,0) + Sum A006319(k)*a(n-k-1,0), k=0..m-1.

1, 1, 2, 4, 5, 9, 16, 20, 24, 40, 68, 84, 100, 116, 184, 304, 372, 436, 500, 568, 872, 1412, 1716, 1988, 2244, 2516, 2820, 4232, 6752, 8164, 9380, 10468, 11556, 12772, 14184, 20936, 33028

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

OFFSET

0,3

COMMENTS

Compare to A073150. Related to Royal paths in a lattice (A006318, A006319).

LINKS

Table of n, a(n) for n=0..36.

FORMULA

a(n, m+1) = a(n, 0) + Sum A006319(k)*a(n-k-1, 0), k=0..m-1.

EXAMPLE

a(4,2)=a(4,0)+1*a(3,0)+4*a(2,0)=68+(1*16+4*4)=100. a(4,0)=a(3,0)+a(3,3)+a(2,2)+a(1,1)+a(0,0)=16+(40+9+2+1)=68. Rows of triangle: {1}, {1,2}, {4,5,9}, {16,20,24,40}, {68,84,100,116,184},{304,372,436,500,568,872}, {1412,1716,1988,2244,2516,2820,4232}, ...

CROSSREFS

Cf. A073150, A006319, A006318.

Sequence in context: A336866 A255213 A226447 * A279786 A255515 A067298

Adjacent sequences: A073148 A073149 A073150 * A073152 A073153 A073154

KEYWORD

easy,nonn,tabl

AUTHOR

Paul D. Hanna, Jul 18 2002

STATUS

approved