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A014825
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a(1)=1, a(n)=4*a(n-1)+n.
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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| A014825 ~ A078904, A014825 * 3 = A078904. [From Vladimir Orlovsky, Mar 21 2009]
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..1000
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FORMULA
| a(n)=(4^(n+1)-3*n-4)/9.
G.f.: x/((1-4*x)*(1-x)^2).
a(n)=sum{k=0..n, (n-k)*4^k}=sum{k=0..n, k*4^(n-k)} - Paul Barry, Jul 30 2004
a(n)=sum{k=0..n, binomial(n+2, k+2)*3^k} [Offset 0] - Paul Barry, Jul 30 2004
a(n)=sum{k=0..n, binomial(n+3, k+3)*3^k} [Offset 0] - Paul Barry, 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, Oct 23 2009]
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MAPLE
| 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
| lst={}; s=0; Do[s+=s+n; s+=s+n; AppendTo[lst, s/6], {n, 0, 5!, 2}]; lst [From Vladimir Orlovsky, Mar 21 2009]
RecurrenceTable[{a[1]==1, a[n]==4a[n-1]+n}, a[n], {n, 30}] (* From Harvey P. Dale, Oct 12 2011 *)
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PROG
| (MAGMA) [(4^(n+1)-3*n-4)/9: n in [1..30]]; // Vincenzo Librandi, Aug 23 2011
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CROSSREFS
| Cf. A053142. [From Paul Barry (pbarry(AT)wit.ie), Oct 23 2009]
Sequence in context: A108958 A005284 A198694 * A141844 A176476 A079742
Adjacent sequences: A014822 A014823 A014824 * A014826 A014827 A014828
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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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