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 A105321 Convolution of binomial(1,n) and Gould's sequence A001316. 10
 1, 3, 4, 6, 6, 6, 8, 12, 10, 6, 8, 12, 12, 12, 16, 24, 18, 6, 8, 12, 12, 12, 16, 24, 20, 12, 16, 24, 24, 24, 32, 48, 34, 6, 8, 12, 12, 12, 16, 24, 20, 12, 16, 24, 24, 24, 32, 48, 36, 12, 16, 24, 24, 24, 32, 48, 40, 24, 32, 48, 48, 48, 64, 96, 66, 6, 8, 12, 12, 12, 16, 24, 20, 12, 16 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A universal function related to the spherical growth of repeated truncations of maps. a(n) = (number of ones in row n of triangle A249133) = (number of odd terms in row n of triangle A249095) = A000120(A249184(n)). - Reinhard Zumkeller, Nov 14 2014 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata, Congressus Numerantium, Vol. 206 (2010), 157-191. [There is a typo in Theorem 6: (13) should read u(n) = 4.3^(wt(n-1)-1) for n >= 2.] T. Pisanski and T. W. Tucker, Growth in Repeated Truncations of Maps, Preprint series, Univ. of Ljubljana, Vol. 38 (2000), 696. T. Pisanski and T. W. Tucker, Growth in Repeated Truncations of Maps, Atti. Sem. Mat. Fis. Univ. Modena, Vol. 49 (2001), 167-176. N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS - Omar E. Pol, May 29 2010 FORMULA G.f. (1+x)*Product{k>=0, 1+2x^(2^k)}; a(n) = Sum_{k=0..n, binomial(1, n-k)*Sum_{j=0..k, binomial(k, j) mod 2}}. a(n) = 2*A048460(n) for n>=2. - Omar E. Pol, Jan 02 2011 a((2*n-1)*2^p) = (2^p+2)*A001316(n-1), p >= 0 and n >= 1, with a(0) = 1. - Johannes W. Meijer, Jan 28 2013 a(n) = A001316(n) + A001316(n-1) for n > 0. - Reinhard Zumkeller, Nov 14 2014 EXAMPLE Contribution from Omar E. Pol, May 29 2010: (Start) If written as a triangle: 1; 3; 4; 6,6; 6,8,12,10; 6,8,12,12,12,16,24,18; 6,8,12,12,12,16,24,20,12,16,24,24,24,32,48,34; 6,8,12,12,12,16,24,20,12,16,24,24,24,32,48,36,12,16,24,24,24,32,48,40,24,32,48,48,48,64,96,66; (End) MAPLE nmax := 74: A001316 := n -> if n <= -1 then 0 else 2^add(i, i=convert(n, base, 2)) fi: for p from 0 to ceil(log[2](nmax)) do for n from 1 to nmax/(p+2)+1 do a((2*n-1)*2^p) := (2^p+2) * A001316(n-1) od: od: a(0) :=1: seq(a(n), n=0..nmax); # Johannes W. Meijer, Jan 28 2013 MATHEMATICA f[n_] := Sum[Binomial[1, n - k]Mod[Binomial[k, j], 2], {k, 0, n}, {j, 0, k}]; Array[f, 75, 0] (* Robert G. Wilson v, Jun 28 2010 *) PROG (Haskell) a105321 n = if n == 0 then 1 else a001316 n + a001316 (n - 1) -- Reinhard Zumkeller, Nov 14 2014 (PARI) a(n) = sum(k=0, n, binomial(1, n-k)*sum(j=0, k, binomial(k, j) % 2)); \\ Michel Marcus, Apr 29 2018 CROSSREFS Cf. A139250, A139251, A173522, A048460. Cf. A001316, A000120, A249184, A249095, A249133. Sequence in context: A298808 A033957 A031131 * A217032 A300305 A160095 Adjacent sequences: A105318 A105319 A105320 * A105322 A105323 A105324 KEYWORD easy,nonn AUTHOR Paul Barry, Apr 01 2005 STATUS approved

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Last modified December 3 09:50 EST 2022. Contains 358517 sequences. (Running on oeis4.)