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Search: id:A014825
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| A014825 |
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a(1)=1, a(n)=4*a(n-1)+n. |
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+0
11
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| 1, 6, 27, 112, 453, 1818, 7279, 29124, 116505, 466030, 1864131, 7456536, 29826157, 119304642, 477218583, 1908874348, 7635497409, 30541989654, 122167958635, 488671834560, 1954687338261, 7818749353066
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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A014825 ~ A078904, A014825 * 3 = A078904. [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 21 2009]
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FORMULA
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G.f.: x/((1-4*x)*(1-x)^2). a(n)=(4^(n+1)-3*n-4)/9.
a(n)=sum{k=0..n, (n-k)4^k}=sum{k=0..n, k*4^(n-k)} - Paul Barry (pbarry(AT)wit.ie), Jul 30 2004
a(n)=sum{k=0..n, binomial(n+2, k+2)3^k} [Offset 0] - Paul Barry (pbarry(AT)wit.ie), Jul 30 2004
a(n)=sum{k=0..n, binomial(n+3, k+3)3^k} [Offset 0] - Paul Barry (pbarry(AT)wit.ie), Aug 20 2004
a(n)=A078904(n)/3 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 27 2007
a(n)=sum{k=0..n, sum{j=0..2k, (-1)^(j+1)*J(j)*J(2k-j)}}, J(n)=A001045(n). [From Paul Barry (pbarry(AT)wit.ie), Oct 23 2009]
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MAPLE
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a:=n->1/3*sum(4^j-1, j=1..n): seq(a(n), n=1..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 27 2007
a:=n->sum(4^(n-j)*j, j=0..n): seq(a(n), n=1..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 07 2008
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MATHEMATICA
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lst={}; s=0; Do[s+=s+n; s+=s+n; AppendTo[lst, s/6], {n, 0, 5!, 2}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 21 2009]
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CROSSREFS
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Cf. A053142. [From Paul Barry (pbarry(AT)wit.ie), Oct 23 2009]
Sequence in context: A003517 A108958 A005284 this_sequence A141844 A079742 A130019
Adjacent sequences: A014822 A014823 A014824 this_sequence A014826 A014827 A014828
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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