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A104585
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Pentagonal wave sequence of the second kind.
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3
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0, 2, 5, 15, 22, 40, 51, 77, 92, 126, 145, 187, 210, 260, 287, 345, 376, 442, 477, 551, 590, 672, 715, 805, 852, 950, 1001, 1107, 1162, 1276, 1335, 1457, 1520, 1650, 1717, 1855, 1926, 2072, 2147, 2301, 2380, 2542, 2625, 2795, 2882, 3060, 3151, 3337, 3432, 3626
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| A104584, pentagonal wave sequence of the first kind; switches odd and even applications and visa versa in A104585. The pentagonal wave triangle, A104586, has A104584 in odd columns and A104585 in even columns.
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FORMULA
| Even index terms are pentagonal numbers with even index in A000326. Odd index terms are second pentagonal numbers with odd index in A005449.
a(n) = (1/2) * [3n^2 - n*(-1)^n ]. - Ralf Stephan, Nov 13 2010.
G.f.: x*(2+3*x+6*x^2+x^3)/(1-x)^3/(1+x)^2. - Colin Barker, Feb 13 2012
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EXAMPLE
| a(5) = 40 = A005449(5), a second pentagonal number.
a(6) = 51 = A000326(6) a pentagonal number.
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CROSSREFS
| Cf. A000326, A005449, A049452, A033570, A049453, A033568, A104586.
Sequence in context: A146121 A066883 A146120 * A146119 A116053 A146118
Adjacent sequences: A104582 A104583 A104584 * A104586 A104587 A104588
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KEYWORD
| nonn,changed
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 17 2005
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EXTENSIONS
| More terms from Colin Barker (c.barker(AT)orange.fr), Feb 13 2012
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