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A122996
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Expansion of (1+6*x)/(1-x-49*x^2).
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4
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1, 7, 56, 399, 3143, 22694, 176701, 1288707, 9947056, 73093699, 560499443, 4142090694, 31606563401, 234569007407, 1783290614056, 13277171976999, 100658412065743, 751239838938694, 5683502030160101, 42494254138156107
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| The sequence is also 7^n times the sum of the top row elements of the n-th power of the 2-by-2 matrix (0,1;1,1/7).
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LINKS
| Nathaniel Johnston, Table of n, a(n) for n = 0..400
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FORMULA
| a(n)=a(n-1)+49*a(n-2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 26 2009]
a(n)=(1/2+13*sqrt(197)/394)*(1/2+sqrt(197)/2)^n+(1/2-13*sqrt(197)/394)*(1/2-sqrt(197)/2)^n. [From Antonio Alberto Olivares, Jun 06 2011]
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MATHEMATICA
| M := {{0, 1}, {1, 1/7}}; v[1] = {1, 1}; v[n_] := v[n] = M.v[n - 1]; a = Table[v[n][[1]]*7^(n - 1), {n, 1, 30}]
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CROSSREFS
| Cf. A122995.
Sequence in context: A082140 A054614 A104896 * A092315 A092318 A057090
Adjacent sequences: A122993 A122994 A122995 * A122997 A122998 A122999
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KEYWORD
| nonn,easy
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AUTHOR
| Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 22 2006
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EXTENSIONS
| Edited by the Associate Editors of the OEIS, Sep 09 2009
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