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Search: id:A125577
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| A125577 |
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a(0) = 1; for n >= 0, a(n+1) = n^2 - a(n). |
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+0
2
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| 1, 0, 4, 5, 11, 14, 22, 27, 37, 44, 56, 65, 79, 90, 106, 119, 137, 152, 172, 189, 211, 230, 254, 275, 301, 324, 352, 377, 407, 434, 466, 495, 529, 560, 596, 629, 667, 702, 742, 779, 821, 860, 904, 945, 991, 1034, 1082, 1127, 1177, 1224, 1276, 1325, 1379, 1430
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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A sequence given by a recurrence that is almost polynomial; it cannot be expressed as a polynomial, but is bounded by n^2.
If we let a(0) = 0, the triangular numbers result; a typo led to the new sequence.
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FORMULA
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O.g.f.: (-1+2*x-4*x^2+x^3)/((-1+x)^3*(1+x)). a(n) = -n-1+(-1)^n+A000217(n+1). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 05 2007
a(n)=(1/2)*[2*(-1)^n+n^2+n], with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Oct 07 2008]
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EXAMPLE
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a(0)=1, so a(1) = 1^2 - 1 = 0; a(2) = 2^2 - 0 = 4; a(3) = 9 - 4 = 5; etc.
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MATHEMATICA
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a[0] := 1 a[n_] := n^2 - a[n - 1]
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CROSSREFS
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Cf. A000217.
Sequence in context: A118423 A084812 A050018 this_sequence A053307 A076065 A066898
Adjacent sequences: A125574 A125575 A125576 this_sequence A125578 A125579 A125580
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KEYWORD
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easy,nonn
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AUTHOR
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John C. George (John.George(AT)ENMU.edu), Jan 03 2007
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