A164855 Generalized Lucas-Pascal triangle: (101*100^n,1)

1, 101, 1, 10100, 102, 1, 1010000, 10202, 103, 1, 101000000, 1020202, 10305, 104, 1, 10100000000, 102020202, 1030507, 10409, 105, 1, 1010000000000, 10202020202, 103050709, 1040916, 10514, 106, 1, 101000000000000, 1020202020202

Offset

0,2

Links

Table of n, a(n) for n=0..29.

Formula

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

Example

Triangle begins:
1
101,1
10100,102,1
1010000,10202,103,1
101000000,1020202,10305,104,1
10100000000,102020202,1030507,10409,105,1
1010000000000,10202020202,103050709,1040916,10514,106,1
101000000000000,1020202020202,10305070911,104091625,1051430,10620,107,1

Maple

A164855 := proc(n, k)
    option remember;
    if n=k then
        1;
    elif k>n or k<0 then
        0;
    elif k = 0 then
        101*100^(n-1) ;
    else
        procname(n-1, k-1)+procname(n-1, k) ;
    end if;
end proc:
seq(seq(A164855(n, k), k=0..n), n=0..12) ; # R. J. Mathar, Nov 03 2016

Crossrefs

Cf. A164847, A164851, A029635, A228196.

Sequence in context: A277917 A281103 A164866 * A284247 A256826 A036193

Adjacent sequences: A164852 A164853 A164854 * A164856 A164857 A164858

Keyword

nonn,tabl,easy

Author

Mark Dols, Aug 28 2009

Extensions

Initial 1 added by Philippe Deléham, Dec 27 2013

Status

approved