A164851 Generalized Lucas-Pascal triangle; (11*10^n, 1).

1, 11, 1, 110, 12, 1, 1100, 122, 13, 1, 11000, 1222, 135, 14, 1, 110000, 12222, 1357, 149, 15, 1, 1100000, 122222, 13579, 1506, 164, 16, 1, 11000000, 1222222, 135801, 15085, 1670, 180, 17, 1

Offset: 0

Author

Mark Dols, Aug 28 2009

Keywords

• nonn
• tabl

Examples

			Triangle begins:
         1;
        11,      1;
       110,     12,      1;
      1100,    122,     13,     1;
     11000,   1222,    135,    14,    1;
    110000,  12222,   1357,   149,   15,   1;
   1100000, 122222,  13579,  1506,  164,  16,  1;
  11000000,1222222, 135801, 15085, 1670, 180, 17, 1;
  ...
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10010(rows 0 to 140, flattened)

Crossrefs

Cf. A029635, A164844, A228196.

Programs

Maple

G[0]:= 1;
G[1]:= 11+x;
G[2]:= 110+12*x+x^2;
for nn from 3 to 20 do
  G[nn]:= expand((x+11)*G[nn-1]-10*(x+1)*G[nn-2]);
od:
seq(seq(coeff(G[n],x,j),j=0..n),n=0..20); # Robert Israel, Jul 17 2017

Mathematica

T[0, 0] := 1; T[n_, n_] := 1; T[n_, 0] := 11*10^(n - 1); T[n_, k_] := T[n - 1, k - 1] + T[n - 1, k];  Table[T[n, k], {n, 0, 10}, {k, 0, n}] //Flatten (* G. C. Greubel, Dec 22 2017 *)

Formula

T(0,0)=1, T(n+1,0)=11*10^n, T(n,n)=1, T(n,k)=T(n-1,k-1)+T(n-1,k) for 0Philippe Deléham, Dec 27 2013

G.f. as triangle: (1-x^2)/((1-10*x)*(1-x-x*y)). - Robert Israel, Jul 17 2017

Extensions

Initial 1 added by Philippe Deléham, Dec 27 2013