A107946 Start with S(0)={1}, then S(k+1) equals the concatenation of S(k) with the partial sums of S(k); the limit gives this sequence.

1, 1, 1, 2, 1, 2, 3, 5, 1, 2, 3, 5, 6, 8, 11, 16, 1, 2, 3, 5, 6, 8, 11, 16, 17, 19, 22, 27, 33, 41, 52, 68, 1, 2, 3, 5, 6, 8, 11, 16, 17, 19, 22, 27, 33, 41, 52, 68, 69, 71, 74, 79, 85, 93, 104, 120, 137, 156, 178, 205, 238, 279, 331, 399, 1, 2, 3, 5, 6, 8, 11, 16, 17, 19, 22, 27, 33

Offset

1,4

Comments

The partial sums is A107947. Terms at positions 2^k forms A107948.

Links

Ivan Neretin, Table of n, a(n) for n = 1..8192

Example

Concatenate the initial 2^3 terms: {1,1,1,2,1,2,3,5} to the partial sums {1,2,3,5,6,8,11,16}
to obtain the initial 2^4 terms: {1,1,1,2,1,2,3,5, 1,2,3,5,6,8,11,16}.

Mathematica

Nest[Join[#, Accumulate@#] &, {1}, 7] (* Ivan Neretin, Jan 31 2018 *)

Prog

(PARI) {a(n)=local(A=[1, 1], B=[1]); for(i=1, #binary(n)-1, B=concat(B, vector(#B, k, polcoeff(Ser(A)/(1-x), #B+k-1))); A=concat(A, B); ); A[n]}

Crossrefs

Cf. A107947, A107948.

Sequence in context: A081664 A224926 A117673 * A054502 A371335 A059346

Adjacent sequences: A107943 A107944 A107945 * A107947 A107948 A107949

Keyword

nonn,look

Author

Paul D. Hanna, May 28 2005

Status

approved