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Search: id:A084221
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| A084221 |
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a(n+2) = 4a(n), with a(0)=1, a(1)=3. |
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+0
14
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| 1, 3, 4, 12, 16, 48, 64, 192, 256, 768, 1024, 3072, 4096, 12288, 16384, 49152, 65536, 196608, 262144, 786432, 1048576, 3145728, 4194304, 12582912, 16777216, 50331648, 67108864, 201326592, 268435456, 805306368, 1073741824, 3221225472
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OFFSET
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0,2
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COMMENT
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Binomial transform is A060925. Binomial transform of A084222.
Sequences with similar recurrence rules: A016116 (multiplier 2), A133626 (multiplier 3), A133632 (multiplier 5). See A133632 for general formulas. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Sep 19 2007
Equals A133080 * A000079. A122756 is a companion sequence. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 19 2007
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FORMULA
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a(n) = (5*2^n-(-2)^n)/4; G.f.: (1+3x)/((1-2x)(1+2x)); E.g.f.: (5exp(2x)-exp(-2x))/4.
a(n) = A133628(n)-A133628(n-1) for n>1. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Sep 19 2007
Equals A133080 * [1, 2, 4, 8,...]. Row sums of triangle A133087 - Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 08 2007
a(n+1)-2a(n) = A000079 signed. a(n)+a(n+2)=5*a(n). First differences give A135520. - Paul Curtz (bpcrtz(AT)free.fr), Apr 22 2008
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CROSSREFS
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For partial sums see A133628. Partial sums for other multipliers p: A027383(p=2), A133627(p=3), A133629(p=5).
Other related sequences: A132666, A132667, A132668, A132669.
Cf. A133080, A133087.
Sequence in context: A047173 A116653 A122757 this_sequence A026847 A026880 A026891
Adjacent sequences: A084218 A084219 A084220 this_sequence A084222 A084223 A084224
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), May 21 2003
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EXTENSIONS
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Edited by njas, Dec 14 2007
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