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Search: id:A157130
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| 1, 4, 8, 13, 20, 29, 40, 53, 68, 84, 101, 120, 141, 164, 189, 216, 245, 276, 309, 344, 380, 417, 456, 497, 540, 585, 632, 681, 732, 785, 840, 897, 956, 1017, 1080, 1144, 1209, 1276, 1345, 1416, 1489, 1564, 1641, 1720, 1801, 1884, 1969, 2056, 2145, 2236, 2329
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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a(n) = (n-r)^2+(4*r^3+6*r^2+2*r)/3 where r = floor((-1+floor(sqrt(1+8*n)))/4).
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EXAMPLE
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For n=3, 1+3+4=8
First three terms of A128201 are 1, 3, 4, hence a(3) = 1+3+4 = 8.
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PROGRAM
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(MAGMA) [ (n-r)^2+(4*r^3+6*r^2+2*r)/3 where r is Floor((-1+Floor(Sqrt(1+8*n)))/4): n in [1..51] ];
(PARI) {for(n=1, 51, r=floor((-1+floor(sqrt(1+8*n)))/4); print1((n-r)^2+(4*r^3+6*r^2+2*r)/3, ", "))}
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CROSSREFS
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Cf. A128201 (union of A000290 and A005408), A000290 (squares), A005408 (odd numbers).
Sequence in context: A143978 A071994 A023661 this_sequence A060403 A139097 A160395
Adjacent sequences: A157127 A157128 A157129 this_sequence A157131 A157132 A157133
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KEYWORD
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nonn
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AUTHOR
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Gerald Hillier (adr.rabbicat(AT)gmail.com), Feb 23 2009
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EXTENSIONS
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Edited and extended by Klaus Brockhaus, Feb 24 2009
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