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A105321
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Convolution of binomial(1,n) and Gould's sequence A001316.
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5
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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; internal format)
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OFFSET
| 0,2
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COMMENTS
| A universal function related to the spherical growth of repeated truncations of maps.
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LINKS
| T. Pisanski and T. W. Tucker, Growth in Repeated Truncations of Maps, Atti. Sem. Mat. Fis. Univ. Modena, Vol. 49 (2001), 167-176.
David Applegate, Omar E. Pol and N. J. A. Sloane, The Toothpick Sequence and Other Sequences from Cellular Automata [From Omar E. Pol (info(AT)polprimos.com), May 29 2010]
T. Pisanski and T. W. Tucker, Growth in Repeated Truncations of Maps, Preprint series, Univ. of Ljubljana, Vol. 38 (2000), 696. [From Omar E. Pol (info(AT)polprimos.com), May 29 2010]
N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS [From Omar E. Pol (info(AT)polprimos.com), May 29 2010]
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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. [From Omar E. Pol (info(AT)polprimos.com), Jan 02 2011]
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EXAMPLE
| Contribution from Omar E. Pol (info(AT)polprimos.com), 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)
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MATHEMATICA
| f[n_] := Sum[Binomial[1, n - k]Mod[Binomial[k, j], 2], {k, 0, n}, {j, 0, k}]; Array[f, 75, 0] [From Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 28 2010]
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CROSSREFS
| Cf. A139250, A139251, A173522. [From Omar E. Pol (info(AT)polprimos.com), May 29 2010]
Cf. A048460 [From Omar E. Pol, Jan 02 2011]
Sequence in context: A198617 A033957 A031131 * A160095 A135319 A004219
Adjacent sequences: A105318 A105319 A105320 * A105322 A105323 A105324
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KEYWORD
| easy,nonn,changed
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Apr 01 2005
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