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Search: id:A134119
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| A134119 |
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a(n) = floor(n^2/10) - floor((n-1)^2/10). |
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+0
1
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| 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 17, 17, 17
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OFFSET
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0,9
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COMMENT
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Note that for n >=1 there is a pattern that keeps steadily alternating between 4 terms and 6 terms for the each two consecutive groups. The terms value remains the same within each 4-term or 6-term group, while during the switch from the 4-group to the 6-group and then back from the 6-group to the 4-group, etc., the term value is getting bumped by 1.
Comment from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jan 16, 2008. Assuming this obeys the recurrence a(n)=a(n-10)+2, this has generating function G(x) = x^4*(1+x^4)/[(-1+x)^2*(x+1)*(x^4+x^3+x^2+x+1)*(x^4-x^3+x^2-x+1)] = (1-3x^2-3x^3)/[10(x^4+x^3+x^2+x+1)]+1/[10(x+1)]+1/[5(-1+x)^2] +(-1+2x-3x^2-x^3)/[10(x^4-x^3+x^2-x+1)]+3/[10(-1+x)]. The first term can be rewritten as a linear superposition of A104384(n), A104384(n+2), A103483(n+3); the second, ~1/(x+1), with the alternating A033999, the third component ~1/(x-1)^2 with a(n)=n+1, the next ~1/(x^4-x^3+x^2-x+1) = A014019, and the last is proportional to 1/(1-x) = A000012. So a(n) is a sum of these sequences.
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PROGRAM
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(PARI) a(n)= floor(n^2/10) - floor((n-1)^2/10)
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CROSSREFS
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Sequence in context: A033271 A004052 A051742 this_sequence A064661 A131996 A090618
Adjacent sequences: A134116 A134117 A134118 this_sequence A134120 A134121 A134122
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KEYWORD
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nonn
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AUTHOR
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Alexander R. Povolotsky (pevnev(AT)juno.com), Jan 12 2008
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EXTENSIONS
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More terms from njas, Jan 22 2008
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