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Generalized Lucas-Pascal triangle: (101*100^n,1)
3

%I #12 Nov 03 2016 05:33:15

%S 1,101,1,10100,102,1,1010000,10202,103,1,101000000,1020202,10305,104,

%T 1,10100000000,102020202,1030507,10409,105,1,1010000000000,

%U 10202020202,103050709,1040916,10514,106,1,101000000000000,1020202020202

%N Generalized Lucas-Pascal triangle: (101*100^n,1)

%F T(0,0)=1, T(n+1,0)=101*100^n, T(n,n)=1, T(n,k)=T(n-1,k-1)+T(n-1,k) for 0<k<n. - _Philippe Deléham_, Dec 27 2013

%e Triangle begins:

%e 1

%e 101,1

%e 10100,102,1

%e 1010000,10202,103,1

%e 101000000,1020202,10305,104,1

%e 10100000000,102020202,1030507,10409,105,1

%e 1010000000000,10202020202,103050709,1040916,10514,106,1

%e 101000000000000,1020202020202,10305070911,104091625,1051430,10620,107,1

%p A164855 := proc(n,k)

%p option remember;

%p if n=k then

%p 1;

%p elif k>n or k<0 then

%p 0;

%p elif k = 0 then

%p 101*100^(n-1) ;

%p else

%p procname(n-1,k-1)+procname(n-1,k) ;

%p end if;

%p end proc:

%p seq(seq(A164855(n,k),k=0..n),n=0..12) ; # _R. J. Mathar_, Nov 03 2016

%Y Cf. A164847, A164851, A029635, A228196.

%K nonn,tabl,easy

%O 0,2

%A _Mark Dols_, Aug 28 2009

%E Initial 1 added by _Philippe Deléham_, Dec 27 2013