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A254138
Pentagonal numbers (A000326) which are also centered hexagonal numbers (A003215).
3
1, 7957, 1185037, 10596309577, 1578130224697, 14111253811878301, 2101618114050816901, 18792154258821103289617, 2798754265133491448134897, 25025774916617575492416996517, 3727140237435880812247465267837, 33327174817289665775049786996211801
OFFSET
1,2
FORMULA
a(n) = a(n-1)+1331714*a(n-2)-1331714*a(n-3)-a(n-4)+a(n-5).
G.f.: -x*(x^4+7956*x^3-154634*x^2+7956*x+1) / ((x-1)*(x^2-1154*x+1)*(x^2+1154*x+1)).
EXAMPLE
7957 is in the sequence because it is the 73rd pentagonal number and the 52nd centered hexagonal number.
MATHEMATICA
LinearRecurrence[{1, 1331714, -1331714, -1, 1}, {1, 7957, 1185037, 10596309577, 1578130224697}, 20] (* Harvey P. Dale, Sep 26 2023 *)
PROG
(PARI) Vec(-x*(x^4+7956*x^3-154634*x^2+7956*x+1)/((x-1)*(x^2-1154*x+1)*(x^2+1154*x+1)) + O(x^100))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jan 26 2015
STATUS
approved