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A130665
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a(n) = Sum_{k=0..n} 3^wt(k), where wt() = A000120().
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11
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1, 4, 7, 16, 19, 28, 37, 64, 67, 76, 85, 112, 121, 148, 175, 256, 259, 268, 277, 304, 313, 340, 367, 448, 457, 484, 511, 592, 619, 700, 781, 1024, 1027, 1036, 1045, 1072, 1081, 1108, 1135, 1216, 1225, 1252, 1279, 1360, 1387, 1468, 1549, 1792, 1801, 1828, 1855
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| D. E. Knuth, Problem submitted to Amer. Math. Monthly, Jun 18 2007.
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LINKS
| O. E. Pol, Illustration of initial terms (Neighbors of the vertices) [From Omar E. Pol (info(AT)polprimos.com), Nov 08 2009]
O. E. Pol, Illustration of initial terms (Overlapping squares) [From Omar E. Pol (info(AT)polprimos.com), Nov 08 2009]
O. E. Pol, Illustration of initial terms (One-step bishop) [From Omar E. Pol (info(AT)polprimos.com), Nov 08 2009]
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FORMULA
| With a different offset: a(1) = 1; a(n) = max { 3*a(k)+a(n-k) | 1 <= k <= n/2 }, for n>1.
a(2n+1) = 4a(n) and a(2n) = 3a(n-1)+a(n).
a(n) = (A147562(n+1)-1)*3/4 + 1. [From Omar E. Pol (info(AT)polprimos.com), Nov 08 2009]
a(n) = A160410(n+1)/4. [From Omar E. Pol (info(AT)polprimos.com), Nov 12 2009]
Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 26 2010: (Start)
Let r(x) = (1 + 4x + 3x^2), then (1 + 4x + 7x^2 + 16x^3 + ...) =
r(x)* r(x^2) * r(x^4) * r(x^8) * ... (End)
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MAPLE
| u:=3; a[1]:=1; M:=30; for n from 1 to M do a[2*n] := (u+1)*a[n]; a[2*n+1] := u*a[n] + a[n+1]; od; t1:=[seq( a[n], n=1..2*M )]; # Gives sequence with a different offset
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MATHEMATICA
| f[n_] := Sum[3^Count[ IntegerDigits[k, 2], 1], {k, 0, n}]; Array[f, 51, 0]
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CROSSREFS
| Cf. A006046, A116520, A130667.
Partial sums of A048883. - David Applegate, Jun 11 2009.
Cf. A147562, A151920, A151922, A160412. [From Omar E. Pol (info(AT)polprimos.com), Nov 08 2009]
Cf. A160410. [From Omar E. Pol (info(AT)polprimos.com), Nov 12 2009]
Sequence in context: A166700 A160715 A160120 * A101534 A110933 A067398
Adjacent sequences: A130662 A130663 A130664 * A130666 A130667 A130668
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), based on a message from D. E. Knuth, Jun 23 2007
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EXTENSIONS
| Simpler definition (and new offset) from David Applegate, Jun 11 2009
I changed the lower limit of the sum in the definition from 1 to 0 and I added the Mathematica coding. - Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 28 2010
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