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Search: id:A081585
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| 1, 9, 33, 73, 129, 201, 289, 393, 513, 649, 801, 969, 1153, 1353, 1569, 1801, 2049, 2313, 2593, 2889, 3201, 3529, 3873, 4233, 4609, 5001, 5409, 5833, 6273, 6729, 7201, 7689, 8193, 8713, 9249, 9801, 10369, 10953, 11553, 12169, 12801, 13449, 14113
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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If A=[A157912] 64*n.^2+16 (80, 272, 592,.,); Y=[A000027] n (1, 2,4,6,8,.,); X=[A081585] 8*n^2 + 1 (n>0, 9, 33, 73..,), we have, for all terms, Pell's equation X^2-A*Y^2=1. Example: 9^2-80 *1\^2=1; 33^2-272*2^2=1; 73^2-592*3^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 09 2009]
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FORMULA
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a(n)=1+8n^2. G.f.: (1+3x)^2/(1-x)^3.
a(n)=16*n+a(n-1)-24 (with a(1)=1) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 16 2009]
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EXAMPLE
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For n=2, a(2)=16*2+1-24=9; n=3, a(3)=16*3+9-24=33; n=4, a(4)=16*4+33-24=73 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 16 2009]
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CROSSREFS
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Cf. A016813, A081586.
Cf. A000027, A157912 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Mar 09 2009]
Sequence in context: A145923 A092562 A103602 this_sequence A101990 A147170 A146823
Adjacent sequences: A081582 A081583 A081584 this_sequence A081586 A081587 A081588
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KEYWORD
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easy,nonn,new
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Mar 23 2003
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