This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A247649 Number of terms in expansion of f^n mod 2, where f = 1/x^2 + 1/x + 1 + x + x^2 mod 2. 11
 1, 5, 5, 7, 5, 17, 7, 19, 5, 25, 17, 19, 7, 31, 19, 25, 5, 25, 25, 35, 17, 61, 19, 71, 7, 35, 31, 41, 19, 71, 25, 77, 5, 25, 25, 35, 25, 85, 35, 95, 17, 85, 61, 71, 19, 91, 71, 77, 7, 35, 35, 49, 31, 107, 41, 121, 19, 95, 71, 85, 25, 113, 77, 103 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS This is the number of cells that are ON after n generations in a one-dimensional cellular automaton defined by the odd-neighbor rule where the neighborhood consists of 5 contiguous cells. LINKS Chai Wah Wu, Table of n, a(n) for n = 0..10000 N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168, 2015 FORMULA The values of a(n) for n in A247647 (or A247648) determine all the values, as follows. Parse the binary expansion of n into terms from A247647 separated by at least two zeros: m_1 0...0 m_2 0...0 m_3 ... m_r 0...0. Ignore any number (one or more) of trailing zeros. Then a(n) = a(m_1)*a(m_2)*...*a(m_r). For example, n = 37_10 = 100101_2 is parsed into 1.00.101, and so a(37) = a(1)*a(5) = 5*17 = 85. This is a generalization of the Run Length Transform. EXAMPLE The first few generations are: ..........X.......... ........XXXXX........ ......X.X.X.X.X...... ....XX..X.X.X..XX.... (f^3) ..X...X...X...X...X.. XXXX.XXX.XXX.XXX.XXXX ... f^3 mod 2 = x^6 + x^5 + x^2 + 1/x^2 + 1/x^5 + 1/x^6 + 1 has 7 terms, so a(3) = 7. From Omar E. Pol, Mar 02 2015: (Start) Also, written as an irregular triangle in which the row lengths are the terms of A011782, the sequence begins: 1; 5; 5,7; 5,17,7,19; 5,25,17,19,7,31,19,25; 5,25,25,35,17,61,19,71,7,35,31,41,19,71,25,77; 5,25,25,35,25,85,35,95,17,85,61,71,19,91,71,77,7,35,35,49,31,107,41,121,19,95,71,85,25,113,77,103; ... (End) It follows from the Generalized Run Length Transform result mentioned in the comments that in each row the first quarter of the terms (and no more) are equal to 5 times the beginning of the sequence itself. It cannot be said that the rows converge (in any meaningful sense) to five times the sequence. - N. J. A. Sloane, Mar 03 2015 PROG (Python) import sympy from functools import reduce from operator import mul x = sympy.symbols('x') f = 1/x**2+1/x+1+x+x**2 A247649_list, g = [1], 1 for n in range(1, 1001):     s = [int(d, 2) for d in bin(n)[2:].split('00') if d != '']     g = (g*f).expand(modulus=2)     if len(s) == 1:         A247649_list.append(g.subs(x, 1))     else:         A247649_list.append(reduce(mul, (A247649_list[d] for d in s))) # Chai Wah Wu, Sep 25 2014 CROSSREFS Cf. A071053, A247647, A247648, A253085, A255490. Sequence in context: A088201 A195380 A139261 * A252655 A021646 A231589 Adjacent sequences:  A247646 A247647 A247648 * A247650 A247651 A247652 KEYWORD nonn AUTHOR N. J. A. Sloane, Sep 25 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 11 14:03 EST 2017. Contains 295884 sequences.