

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.


7



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
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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)/(1x), #B+k1))); A=concat(A, B); ); A[n]}


CROSSREFS

Cf. A107947, A107948.
Sequence in context: A081664 A224926 A117673 * A054502 A059346 A259439
Adjacent sequences: A107943 A107944 A107945 * A107947 A107948 A107949


KEYWORD

nonn,look


AUTHOR

Paul D. Hanna, May 28 2005


STATUS

approved



