A007824 a(n) = f(a(n-1)), with f(m) = Sum i*b(i)*2^(i-1), m = Sum b(i)*2^i, and starting value 16.

16, 32, 80, 224, 720, 2976, 15120, 92448, 704592, 6455520, 69518032, 897158048, 12700875536, 203746961696, 3674124288080, 74060581880032, 1692860294726352, 42020514867170208, 1144626896435067664, 33222330682700081440

Offset: 0

Author

Ralph Buchholz [ ralph(AT)defcen.gov.au ], Leisa Condie

Keywords

• nonn

Comments

Previous name was : For N=Sum a(i).2^i, a(i)=0,1, set D(N)/D(2)=Sum i.a(i).2^(i-1); sequence gives n-th derivative of 16.

Actually, it appears that f(n) for n=0, 1, 2, ... gives 0, 0, 1, 1, 4, 4, 5, 5, 12, 12, 13, 13, 16, 16, 17, 17, 32, 32, 33, 33, 36, ... that is A136013. - Michel Marcus, Jul 18 2013 [This now follows from the comments in A136013. - Pontus von Brömssen, Sep 06 2020]

Crossrefs

Cf. A007823, A136013.

Programs

PARI

D(n) = {b = binary(n); lb = #b; rb = vector(lb, i, b[lb-i+1]); return(sum (i=0, lb-1, i*2^(i-1)*rb[i+1]));}
lista(nn) = {m = 16; for (n=0, nn, print1(m, ", "); m = D(m););} \\ Michel Marcus, Jul 18 2013

Formula

a(n) = 16*A007823(n). - Pontus von Brömssen, Sep 06 2020

Extensions

Edited by Michel Marcus, Jul 18 2013