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A105635
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Pell(n+2)/2-(1+(-1)^n)/4.
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3
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0, 1, 2, 6, 14, 35, 84, 204, 492, 1189, 2870, 6930, 16730, 40391, 97512, 235416, 568344, 1372105, 3312554, 7997214, 19306982, 46611179, 112529340, 271669860, 655869060, 1583407981, 3822685022, 9228778026, 22280241074, 53789260175
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Transform of Pell(n) under the Riordan array (1/(1-x^2),x).
Starting (1, 2, 6, 14, 35,...) equals row sums of triangle A157901 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 08 2009]
Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 03 2010: (Start)
Starting with 1 = row sums of a triangle with the Pell series shifted down
twice for columns >1. (End)
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FORMULA
| G.f.: x/((1-x^2)(1-2x-x^2)); a(n)=2a(n-1)+2a(n-2)-2a(n-3)-a(n-4); a(n)=sum{k=0..floor((n-1)/2), Pell(n-2k)}; a(n)=sum{k=0..n, Pell(k)*(1-(-1)^(n+k-1))/2};
a(n) = term (4,1) in the 4x4 matrix [1,1,0,0; 3,0,1,0; 1,0,0,0; 1,0,0,1]^n. - Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 24 2008
a(n)= ( A033539(n+3)- A097076(n+3))/2 [From Gary Detlefs (gdetlefs(AT) aol.com) Dec 19 2010]
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MAPLE
| seq(iquo(fibonacci(n, 2), 2), n=1..30); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 20 2008
a := n -> (Matrix([[1, 1, 0, 0], [3, 0, 1, 0], [1, 0, 0, 0], [1, 0, 0, 1]])^(n))[4, 1]; seq (a(n), n=0..50); - Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 24 2008
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CROSSREFS
| Cf. A000129.
A157901 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 08 2009]
Sequence in context: A099425 A186523 A177790 * A178320 A025257 A110152
Adjacent sequences: A105632 A105633 A105634 * A105636 A105637 A105638
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Apr 16 2005
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