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A084101
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Expansion of (1+x)^2/((1-x)(1+x^2)).
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7
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1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 1, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Partial sums of A084099. Inverse binomial transform of A000749 (without leading zeros).
Contribution from Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 31 2010: (Start)
Periodic sequence: Repeat 1, 3, 3, 1.
Interleaving of A010684 and A176040.
Continued fraction expansion of (7+5*sqrt(29))/26.
Decimal expansion of 121/909.
a(n) = A143432(n+3)+1 = 2*A021913(n+1)+1 = 2*A133872(n+3)+1.
a(n) = A165207(n+1)-1.
First differences of A047538.
Binomial transform of A084102. (End)
Contribution from Wolfdieter Lang, Feb 09 2012: (Start)
a(n) = A045572(n+1) (Mod 5) := A203571(A045572(n+1)), n>=0.
For general Modd n (not to be confused with mod n) see a comment on A203571. The nonnegative members of the five residue classes Modd 5, called [m] for m=0,1,...,4, are shown in the array A090298 if there the last row is taken as class [0] after inclusion of 0.
(End)
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,-1,1).
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FORMULA
| a(n)=binomial(3, mod(n, 4)) - Paul Barry (pbarry(AT)wit.ie), May 25 2003
Contribution from Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 31 2010: (Start)
a(n) = a(n-4) for n > 3; a(0) = a(3) = 1, a(1) = a(2) = 3.
a(n) = (4-(1+I)*I^n-(1-I)*(-I)^n)/2 where I = sqrt(-1). (End)
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EXAMPLE
| Contribution from Wolfdieter Lang, Feb 09 2012: (Start)
Modd 5 of nonnegative odd numbers restricted mod 5:
A045572: 1, 3, 7, 9, 11, 13, 17, 19, 21, 23, ...
Modd 5: 1, 3, 3, 1, 1, 3, 3, 1, 1, 3, ...
(End)
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CROSSREFS
| Cf. A084102.
Cf. A010684 (repeat 1, 3), A176040 (repeat 3, 1), A178593 (decimal expansion of (7+5*sqrt(29))/26), A143432 (expansion of (1+x^4)/((1-x)*(1+x^2))), A021913 (repeat 0, 0, 1, 1), A133872 (repeat 1, 1, 0, 0), A165207 (repeat 2, 2, 4, 4), A047538 (congruent to 0, 1, 4 or 7 mod 8), A084099 (expansion of (1+x)^2/(1+x^2)), A000749 (expansion of x^3/((1-x)^4-x^4)). [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), May 31 2010]
Sequence in context: A126717 A124039 A096433 * A053386 A090569 A160324
Adjacent sequences: A084098 A084099 A084100 * A084102 A084103 A084104
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KEYWORD
| easy,nonn,changed
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 15 2003
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