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A080923
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First differences of A003946.
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3
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1, 3, 8, 24, 72, 216, 648, 1944, 5832, 17496, 52488, 157464, 472392, 1417176, 4251528, 12754584, 38263752, 114791256, 344373768, 1033121304, 3099363912, 9298091736, 27894275208, 83682825624, 251048476872, 753145430616
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Sum of consecutive pairs of elements of A025192.
The alternating sign sequence with g.f. (1-x^2)/(1+3x) gives the row sums of A110168. - Paul Barry (pbarry(AT)wit.ie), Jul 14 2005
Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 18 2010: (Start)
Let M = an infinite lower triangular matrix with the odd integers (1,3,5,...)
in every column, with the leftmost column shifted up one row. Then A080923 =
Lim_{n->inf} M^n. (End)
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FORMULA
| G.f.: (1-x^2)/(1-3*x).
G.f.: 1/(1 - 3*x + x^2 - 3*x^3 + x^4 - 3*x^5 + ...) [Gary W. Adamson, Jan 06 2011].
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MAPLE
| with(combstruct):ZL0:=S=Prod(Sequence(Prod(a, Sequence(b))), a):ZL1:=Prod(begin_blockP, Z, end_blockP):ZL2:=Prod(begin_blockLR, Z, Sequence(Prod(mu_length, Z), card>=1), end_blockLR): ZL3:=Prod(begin_blockRL, Sequence(Prod(mu_length, Z), card>=1), Z, end_blockRL):Q:=subs([a=Union(ZL1, ZL2, ZL3), b=ZL1], ZL0), begin_blockP=Epsilon, end_blockP=Epsilon, begin_blockLR=Epsilon, end_blockLR=Epsilon, begin_blockRL=Epsilon, end_blockRL=Epsilon, mu_length=Epsilon:temp15:=draw([S, {Q}, unlabelled], size=16):seq(count([S, {Q}, unlabelled], size=n), n=1..26); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 08 2008
with(finance):seq(ceil(futurevalue(8, 2, n)), n=-2..23); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 25 2009]
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CROSSREFS
| Essentially the same as A005051, A026097 and A083583.
Sequence in context: A052855 A133787 * A118264 A006365 A178543 A046919
Adjacent sequences: A080920 A080921 A080922 * A080924 A080925 A080926
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Feb 26 2003
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