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A060999
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Nearest integer to (n+1)^3/9.
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3
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0, 1, 3, 7, 14, 24, 38, 57, 81, 111, 148, 192, 244, 305, 375, 455, 546, 648, 762, 889, 1029, 1183, 1352, 1536, 1736, 1953, 2187, 2439, 2710, 3000, 3310, 3641, 3993, 4367, 4764, 5184, 5628, 6097, 6591, 7111, 7658, 8232, 8834, 9465, 10125, 10815, 11536
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,1000
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FORMULA
| G.f.: x*(1+x^2)/((1-x)^3*(1-x^3)).
Expansion of x * (1 - x^4) / ((1 - x)^3 * (1 - x^2) * (1 - x^3)) in powers of x.
Euler transform of length 4 sequence [ 3, 1, 1, -1]. - Michael Somos Aug 12 2009
a(-2-n) = -a(n). - Michael Somos Aug 12 2009.
G.f.: ( (1 + 4*x + x^2) / (1 - x)^4 - 1 / (1 + x + x^2) ) / 9.
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EXAMPLE
| x + 3*x^2 + 7*x^3 + 14*x^4 + 24*x^5 + 38*x^6 + 57*x^7 + 81*x^8 + ...
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PROG
| (PARI) { default(realprecision, 100); for (n=0, 1000, write("b060999.txt", n, " ", round((n + 1)^3/9)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 16 2009]
(PARI) {a(n) = n++; (n^3 - kronecker(-3, n)) / 9} /* Michael Somos Aug 12 2009 */
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CROSSREFS
| Sequence in context: A093523 A173247 A123386 * A089187 A179178 A171973
Adjacent sequences: A060996 A060997 A060998 * A061000 A061001 A061002
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), May 14 2001
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