The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A244643 Number of cells with state 1 at n-th stage in some 2D reversible second order cellular automata (see comments for precise definition). 7
 0, 1, 4, 5, 16, 9, 20, 21, 64, 25, 36, 29, 80, 41, 84, 85, 256, 89, 100, 61, 144, 65, 116, 109, 320, 121, 164, 125, 336, 169, 340, 341, 1024, 345, 356, 189, 400, 161, 244, 205, 576, 209, 260, 181, 464, 225, 436, 429, 1280, 441, 484, 285, 656, 289, 500, 461, 1344, 505, 676, 509, 1360, 681, 1364, 1365, 4096, 1369 (list; graph; refs; listen; history; text; internal format)
 OFFSET -1,3 COMMENTS Consider cellular automata with two states defined in A244642 and second order cellular automata with four states generated from them. If we start with a single cell with state 1 and all the others 0, then number cells with state 1 in subsequent steps will be the terms in the sequence a(n). Number of cells with state 2 is a(n-1), where a(-1) = 0. Equals row 4 in the array shown in A178568. LINKS Alexander Yu. Vlasov, Table of n, a(n) for n = -1..10000 Alexander Yu. Vlasov, Snakes and fractals Alexander Yu. Vlasov, Nine initial patterns Alexander Yu. Vlasov, On number of nonzero cells in some two-dimensional reversible second-order cellular automata, arXiv:1407.6553 [math.CO], 2014. FORMULA a(-1) = 0, a(0) = 1, a(2^k + j) = 4*a(j) + a(2^k - j - 2). a(n-1)+a(n) = A244642(n). a(2n+1) = 4a(n), a(2n+2) = a(n+1) + a(n). G.f.: Product_{k>=0} (1 + 4*x^(2^k) + x^(2^(k+1))). - Ilya Gutkovskiy, Mar 16 2021 EXAMPLE For n=4, a(4) = 16 and a(n-1) = a(3) = 5. ....1 ...121 ..1.1.1 .1212121 ..1.1.1 ...121 ....1 MATHEMATICA msb[1]=1; msb[n_] := 2 msb[Quotient[n, 2]]; a[-1] = 0; a[0] = 1; a[n_] := 4 a[n-msb[n]] + a[2 msb[n]-n-2]; Table[a[n], {n, -1, 64}] (* recursion *) Table[PolynomialMod[Fibonacci[n, f]/.f->(x+1/x+y+1/y), 2], {n, 0, 24}]/.{x->1, y->1} (* calculation using GF(2) polynomial representation of CA *) PROG (AXIOM) msb n == if n=1 then 1 else 2*msb(quo(n, 2)) a n == if n<1 then n+1 else 4*a(n-msb(n))+a(2*msb(n)-n-2) [a(n) for n in -1..64] CROSSREFS Cf. A102376, A147562, A244642, A237711, A168081, A178590, A178568. Sequence in context: A340850 A249113 A166590 * A085768 A166304 A078713 Adjacent sequences: A244640 A244641 A244642 * A244644 A244645 A244646 KEYWORD nonn AUTHOR Alexander Yu. Vlasov, Jul 03 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 29 00:02 EST 2023. Contains 359905 sequences. (Running on oeis4.)