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A011377
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Expansion of 1/((1-x)*(1-2*x)*(1-x^2)).
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9
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1, 3, 8, 18, 39, 81, 166, 336, 677, 1359, 2724, 5454, 10915, 21837, 43682, 87372, 174753, 349515, 699040, 1398090, 2796191, 5592393, 11184798, 22369608, 44739229, 89478471, 178956956, 357913926
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index to sequences with linear recurrences with constant coefficients, signature (3,-1,-3,2)
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FORMULA
| a(n) = sum(k=0..n+2, floor((n-k+2)/2)2^k ) = sum(k=0..n+2, floor(k/2)*2^(n-k+2) ). - Paul Barry, Jul 29 2004
a(n)=sum(k=0..floor((n+2)/2), binomial(n-k+2, k+2)*2^k ). - Paul Barry, Oct 25 2004
a(n) = [(2^(n+4)-3*n-6)/6] - David W. Wilson, Feb 26 2006
a(n) = (2^(n+5)-6n-21+(-1)^n)/12 - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Dec 02 2006
Row sums of triangle A135086 - Gary W. Adamson, Nov 18 2007
a(n) = 3*a(n-1)-a(n-2)-3*a(n-3)+2*a(n-4). - Paul Curtz, Jul 29 2008
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MATHEMATICA
| Join[{a=1, b=3}, Table[c=1*b+2*a+n; a=b; b=c, {n, 3, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 29 2011*)
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PROG
| (MAGMA) [Floor((2^(n+4)-3*n-6)/6): n in [0..40]]; // Vincenzo Librandi, Aug 14 2011
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CROSSREFS
| Partial sums of A000975. Second partial sums of A001045.
Cf. A135086.
Sequence in context: A117727 A117713 A128552 * A178420 A036385 A196534
Adjacent sequences: A011374 A011375 A011376 * A011378 A011379 A011380
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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