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1, 6, 17, 40, 87, 182, 373, 756, 1523, 3058, 6129, 12272, 24559, 49134, 98285, 196588, 393195, 786410, 1572841, 3145704, 6291431, 12582886, 25165797, 50331620, 100663267, 201326562, 402653153, 805306336, 1610612703, 3221225438
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Characteristic polynomial of M = x^3 - 4x^2 + 5x - 2.
Recursive sequence generated from a 3X3 matrix.
No exponentiation is needed! [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 10 2008]
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FORMULA
| a(0)=1, a(1)=6, a(2)=17 and for n>2, a(n)= 4*a(n-1) - 5*a(n-2) + 2*a(n-3).
a(n) = right term in M^n * [1 1 1]. M^n * [1 1 1] = [1 A033484(n) a(n)].
Row sums of triangle A135855 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 01 2007
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EXAMPLE
| a(5) = 182 = 4*87 - 5*40 + 2*17 = 4*a(4) - 5*a(3) + 2*a(2).
a(5) = 182 = right term in M^5 * [1 1 1]; where M^5 * [ 1 1 1] = [1 94 182] = [1 A033484(5) a(5)].
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MATHEMATICA
| a[0] = 1; a[1] = 6; a[2] = 17; a[n_] := a[n] = 4a[n - 1] - 5a[n - 2] + 2a[n - 3]; Table[ a[n], {n, 0, 30}] (from Robert G. Wilson v JAn 12 2005)
...and/or... s=1; lst={}; Do[s+=(s-n); AppendTo[lst, Abs[s]], {n, 3, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 10 2008]
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PROG
| (PARI) a(n)=if(n==1, 1, if(n==2, 6, if(n==3, 17, 4*a(n-1)-5*a(n-2)+2*a(n-3)))) (Klasen)
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CROSSREFS
| Cf. A033484, A101946.
Cf. A135855.
Sequence in context: A085278 A080275 A061349 * A013319 A047861 A171507
Adjacent sequences: A101942 A101943 A101944 * A101946 A101947 A101948
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KEYWORD
| nonn,easy
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 22 2004
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EXTENSIONS
| More terms from Lambert Klasen (Lambert.Klasen(AT)gmx.net), Jan 06 2005
New definition from Ralf Stephan, May 17 2007
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