0,2

Binary analogue of A003590. More generally, this sequence is the 2nd row of the matrix whose k-th row is the concatenation of the base k expression of n-th row of Pascal's triangle. The 10th row of that array is A003590. The array begins: k/n..1..2...3....4........5................ 1.|..1..11..1111.11111111.1111111111111111.2^(n-1) repetitions of 1. 2.|..1..11..1101.111111...11001101001...... 3.|..1..11..121..110101...11120111......... 4.|..1..11..121..1331.....11012101......... 5.|..1..11..121..1331.....141141........... 6.|..1..11..121..1331.....14641............

a(n) = Concatenate[k=1,n]binomial(n, k) (base 2). a(n) = Concatenate[i=A000217(n),A000217(n+1)] A007088(A007318(i)).

a(0) = 1 because the 0-th row of Pascal's triangle is 1.

a(1) = 11 because the 1st row of Pascal's triangle is 1,1 which concatenates to 11.

a(2) = 1101 because the 2nd row of Pascal's triangle is 1,2,1 which in binary is 1,10,1 which concatenates to 1101.

a(3) = 111111 because the 3rd row of Pascal's triangle is 1,3,3,1 which in binary is 1,11,11,1 which concatenates to 111111.

a(4) = 110010101001 because the 4th row of Pascal's triangle is 1,4,6,4,1 which in binary is 1,100,110,100,1 which concatenates to 11001101001.

a(5) = 1101101010101011 because the 5th row of Pascal's triangle is 1,5,10,10,5,1 which in binary is 1,101,1010,1010,101,1 which concatenates to 1101101010101011.

a(6) = 111011111010011111101 because the 5th row of Pascal's triangle is 1,6,15,20,15,6,1 which in binary is 1,110,1111,10100,1111,110,1 which concatenates to 111011111010011111101.

catL := proc(L) local resul, a ; resul:=0 ; for a in L do resul := resul*10^(max(ilog10(a)+1, 1))+a ; od: RETURN(resul) ; end: A133342 := proc(n) local prow, k ; prow := [1] ; for k from 1 to n do prow := [op(prow), convert(binomial(n, k), binary) ] ; od: catL(prow) ; end: seq(A133342(n), n=0..11) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 08 2008

Cf. A000217, A003590, A007318.

Sequence in context: A090814 A109217 A109227 this_sequence A110574 A127851 A135656

Adjacent sequences: A133339 A133340 A133341 this_sequence A133343 A133344 A133345

base,easy,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 20 2007

Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 08 2008