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Search: id:A095151
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| A095151 |
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a(n+3) = 3*a(n+2) - 2*a(n+1) + 1, given a(0) = 0, a(1) = 2. |
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+0
5
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| 0, 2, 7, 18, 41, 88, 183, 374, 757, 1524, 3059, 6130, 12273, 24560, 49135, 98286, 196589, 393196, 786411, 1572842, 3145705, 6291432, 12582887, 25165798, 50331621, 100663268, 201326563, 402653154, 805306337, 1610612704, 3221225439
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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A sequence generated from a Bell difference row matrix, companion to A095150.
A095150 uses the same recursion rule but the multiplier [1 1 1] instead of [1 0 0].
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FORMULA
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Let M = a 3 X 3 matrix having Bell triangle difference terms (A095149 is comprised of differences of the Bell triangle A011971): (fill in the 3 X 3 matrix with zeros): [1 0 0 / 1 1 0 / 2 1 2] = M. Then M^n * [1 0 0] = [1 n a(n)].
a(n) =3*2^n-n-3 =2*a(n-1)+n+1 =A000295(n+2)-A000079(n). For n>0, a(n)=A077802 (n). - Henry Bottomley (se16(AT)btinternet.com), Oct 25 2004
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EXAMPLE
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a(6) = 183 = 3*88 -2*41 + 1.
a(4) = 41 since M^4 * [1 0 0] = [1 4 41].
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MAPLE
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a[0]:=0:a[1]:=0:for n from 2 to 50 do a[n]:=2*a[n-1]+n od: seq(a[n], n=1..31); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 22 2008
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MATHEMATICA
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a[n_] := (MatrixPower[{{1, 0, 0}, {1, 1, 0}, {2, 1, 2}}, n].{{1}, {0}, {0}})[[3, 1]]; Table[ a[n], {n, 30}] (from Robert G. Wilson v Jun 05 2004)
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CROSSREFS
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Cf. A095149, A095150, A011971, A000110.
Sequence in context: A054111 A055503 A077802 this_sequence A007991 A037294 A076857
Adjacent sequences: A095148 A095149 A095150 this_sequence A095152 A095153 A095154
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), May 30 2004
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EXTENSIONS
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Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 05 2004
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