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A121338
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Pentagonal numbers P(k) that are one-third of other pentagonal numbers: P(k) such that 3*P(k)=P(m) for some m>k.
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3
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70, 511258935, 3732600255368600, 27250975409595074561065, 198953975772318806945317308330, 1452523584226469439408576900215922395, 10604587088767577582197244731443261336155260, 77421990626847055423676582260371016672624778798925
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OFFSET
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1,1
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COMMENTS
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The k values are (A001835(6n-2)+1)/6, the m values are (A001834(6n-3)+1)/6.
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LINKS
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FORMULA
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a(n) = 7300803*a(n-1)-7300803*a(n-2)+a(n-3). - Colin Barker, Jun 20 2015
G.f.: -5*x*(x^2+40545*x+14) / ((x-1)*(x^2-7300802*x+1)). - Colin Barker, Jun 20 2015
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EXAMPLE
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a(1) = ((A001835(4))^2-1)/24 = (41^2-1)/24 = 70; this number and 3*70=210 are pentagonal numbers (in A000326).
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MATHEMATICA
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CoefficientList[Series[5 (x^2 + 40545 x + 14)/((1 - x) (x^2 - 7300802 x + 1)), {x, 0, 20}], x] (* Vincenzo Librandi, Jun 21 2015 *)
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PROG
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(PARI) Vec(-5*x*(x^2+40545*x+14)/((x-1)*(x^2-7300802*x+1)) + O(x^20)) \\ Colin Barker, Jun 20 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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