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 A122554 Let S(1) = {1} and, for n>1 let S(n) be the smallest set containing x, 2x and x+2 for each element x in S(n-1). a(n) is the number of elements in S(n). 7
 1, 3, 6, 10, 15, 23, 35, 54, 84, 132, 209, 333, 533, 856, 1378, 2222, 3587, 5795, 9367, 15146, 24496, 39624, 64101, 103705, 167785, 271468, 439230, 710674, 1149879, 1860527, 3010379, 4870878, 7881228, 12752076, 20633273, 33385317, 54018557, 87403840, 141422362 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS If the set mapping has x -> x,2x,x^2 is used instead of x -> x,x+2,2x, the corresponding sequence consists of the Fibonacci numbers 1,2,3,5,8,... Apparently a(n)= 3*a(n-1) -2*a(n-2) -a(n-3) +a(n-4) for n>6, equivalent to a(n)=A000032(n)+n-1 for n>2. - R. J. Mathar, Nov 18 2009 LINKS Chai Wah Wu, Table of n, a(n) for n = 1..43 FORMULA Empirical g.f.: -x*(x^5-x^4-x^3-x^2+1) / ((x-1)^2*(x^2+x-1)). - Colin Barker, Nov 06 2014 EXAMPLE Under the indicated set mapping we have {1} -> {1,2,3} -> {1,2,3,4,5,6} -> {1,2,3,4,5,6,7,8,10,12}, ..., so a(2)=3, a(3)=6, a(4)=10, etc. MATHEMATICA Do[ Print@ Length@ Nest[ Union@ Flatten[ # /. a_Integer -> {a, 2a, a + 2}] &, {1}, n], {n, 0, 32}] (* Robert G. Wilson v, Sep 27 2006 *) PROG (Python) from sympy import chain, islice def A122554_gen(): # generator of terms s = {1} while True: yield len(s) s = set(chain.from_iterable((x, x+2, 2*x) for x in s)) A122554_list = list(islice(A122554_gen(), 24)) # Chai Wah Wu, Jan 12 2022 CROSSREFS Sequence in context: A262927 A063542 A294413 * A111734 A117457 A024674 Adjacent sequences: A122551 A122552 A122553 * A122555 A122556 A122557 KEYWORD nonn,more AUTHOR John W. Layman, Sep 20 2006 EXTENSIONS a(17)-a(33) from Robert G. Wilson v, Sep 27 2006 a(34)-a(36) from Jinyuan Wang, Apr 14 2020 a(37)-a(39) from Chai Wah Wu, Jan 12 2022 STATUS approved

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Last modified December 1 23:26 EST 2023. Contains 367503 sequences. (Running on oeis4.)