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A254710 Indices of centered square numbers (A001844) which are also pentagonal numbers (A000326). 3
1, 2, 9, 22, 119, 300, 1651, 4172, 22989, 58102, 320189, 809250, 4459651, 11271392, 62114919, 156990232, 865149209, 2186591850, 12049974001, 30455295662, 167834486799, 424187547412, 2337632841179, 5908170368100, 32559025289701, 82290197605982 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Also positive integers y in the solutions to 3*x^2 - 4*y^2 - x + 4*y - 2 = 0, the corresponding values of x being A254709.
LINKS
FORMULA
a(n) = a(n-1)+14*a(n-2)-14*a(n-3)-a(n-4)+a(n-5).
G.f.: x*(x^3+7*x^2-x-1) / ((x-1)*(x^2-4*x+1)*(x^2+4*x+1)).
EXAMPLE
9 is in the sequence because the 9th centered square number is 145, which is also the 10th pentagonal number.
PROG
(PARI) Vec(x*(x^3+7*x^2-x-1)/((x-1)*(x^2-4*x+1)*(x^2+4*x+1)) + O(x^100))
CROSSREFS
Sequence in context: A025176 A032315 A032224 * A193758 A368626 A032149
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Feb 06 2015
STATUS
approved

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Last modified June 23 14:31 EDT 2024. Contains 373651 sequences. (Running on oeis4.)