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Search: id:A097602
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| A097602 |
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a(n+1) = a(n) + number of squares so far; a(1) = 1. |
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+0
4
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| 1, 2, 3, 4, 6, 8, 10, 12, 14, 16, 19, 22, 25, 29, 33, 37, 41, 45, 49, 54, 59, 64, 70, 76, 82, 88, 94, 100, 107, 114, 121, 129, 137, 145, 153, 161, 169, 178, 187, 196, 206, 216, 226, 236, 246, 256, 267, 278, 289, 301, 313, 325, 337, 349, 361, 374, 387, 400, 414, 428
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Conjecture: a(n) = m^2 iff m mod 3 > 0.
a(n) is a square iff n is congruent to {1, 4} mod 9. - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 30 2004
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FORMULA
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a(9*n+1) = (3*n+1)^2; a(9*n+4) = (3*n+2)^2. - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 30 2004
G.f.: x*(1+x^4-x^9+x^10)/((1+x+x^2)*(1+x^3+x^6)*(1-x)^3). - Vladeta Jovovic (vladeta(AT)eunet.rs), Aug 30 2004
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EXAMPLE
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a(2) = a(1) + #{1} = 1 + 1 = 2;
a(3) = a(2) + #{1} = 2 + 1 = 3;
a(4) = a(3) + #{1} = 3 + 1 = 4;
a(5) = a(4) + #{1,4} = 4 + 2 = 6;
a(6) = a(5) + #{1,4} = 6 + 2 = 8;
a(7) = a(6) + #{1,4} = 8 + 2 = 10;
a(8) = a(7) + #{1,4} = 10 + 2 = 12;
a(9) = a(8) + #{1,4} = 12 + 2 = 14;
a(10) = a(9) + #{1,4} = 14 + 2 = 16;
a(11) = a(10) + #{1,4,16} = 16 + 3 = 19;
a(12) = a(11) + #{1,4,16} = 19 + 3 = 22.
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CROSSREFS
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Cf. A101135, A096777.
Sequence in context: A047894 A113769 A056865 this_sequence A126794 A011862 A122957
Adjacent sequences: A097599 A097600 A097601 this_sequence A097603 A097604 A097605
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 30 2004
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