

A073150


Triangle of numbers {a(n,k), n >= 0, 0<=k<=n} defined by a(0,0)=1, a(1,0)=2, a(n,0)=A006318(n), a(n,n)=A006319(n), a(n+1,0)=a(n,0)+a(n,n), a(n,m+1)= Sum A006318(k)*a(nk,0), k=0..m.


1



1, 2, 4, 6, 10, 16, 22, 34, 46, 68, 90, 134, 170, 214, 304, 394, 574, 706, 838, 1018, 1412, 1806, 2594, 3134, 3618, 4158, 4946, 6752, 8558, 12170, 14534, 16514, 18494, 20858, 24470, 33028, 41586
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,2


COMMENTS

Compare to A073151. Related to Royal paths in a lattice (A006318, A006319).


LINKS

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


FORMULA

a(n, m+1) = Sum A006318(k)*a(nk, 0), k=0..m.


EXAMPLE

a(4,2)=1*a(3,0)+2*a(2,0)+6*a(1,0)=1*90+2*22+6*6=170. a(4,0)=1+a(3,3)+a(2,2)+a(1,1)+a(0,0)=1+(68+16+4+1)=90. {1}, {2,4}, {6,10,16}, {22,34,46,68}, {90,134,170,214,304},{394,574,706,838,1018,1412}, {1806,2594,3134,3618,4158,4946,6752}, ...


CROSSREFS

Cf. A073151, A006318, A006319.
Sequence in context: A101176 A192447 A131882 * A076529 A323283 A279715
Adjacent sequences: A073147 A073148 A073149 * A073151 A073152 A073153


KEYWORD

easy,nonn,tabl


AUTHOR

Paul D. Hanna, Jul 18 2002


STATUS

approved



