A164847 (100^n,1) Pascal triangle

1, 100, 1, 10000, 101, 1, 1000000, 10101, 102, 1, 100000000, 1010101, 10203, 103, 1, 10000000000, 101010101, 1020304, 10306, 104, 1, 1000000000000, 10101010101, 102030405, 1030610, 10410, 105, 1, 100000000000000, 1010101010101

Offset

0,2

Comments

(For row n=0,1,2,3,4,5 : Sum of digits = Pascal triangle)

Links

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

Formula

T(n,0)=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

T(n,k)=101*T(n-1,k)+T(n-1,k-1)-100*T(n-2,k)-100*T(n-2,k-1), T(0,0)=1, T(1,0)=100, T(1,1)=1, T(n,k)=0 if k<0 or if k>n. - Philippe Deléham, Dec 27 2013

Example

Triangle begins:
1
100,1
10000,101,1
1000000,10101,102,1
100000000,1010101,10203,103,1
10000000000,101010101,1020304,10306,104,1
1000000000000,10101010101,102030405,1030610,10410,105,1
100000000000000,1010101010101,10203040506,103061015,1041020,10515,106,1
10000000000000000,101010101010101,1020304050607,10306101521,104102035,1051535,10621,107,1,

Crossrefs

Cf. A228196

Sequence in context: A173183 A172179 A147804 * A273479 A333399 A069037

Adjacent sequences: A164844 A164845 A164846 * A164848 A164849 A164850

Keyword

nonn,tabl,easy

Author

Mark Dols, Aug 28 2009

Status

approved