A253411
Indices of centered octagonal numbers (A016754) which are also centered pentagonal numbers (A005891).
Original entry on oeis.org
1, 76, 646, 108871, 930811, 156991186, 1342228096, 226381180621, 1935491982901, 326441505463576, 2790978097114426, 470728424497295251, 4024588480547018671, 678790061683594287646, 5803453797970703808436, 978814798219318465489561, 8368576352085274344745321
Offset: 1
76 is in the sequence because the 76th centered octagonal number is 22801, which is also the 96th centered pentagonal number.
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LinearRecurrence[{1,1442,-1442,-1,1},{1,76,646,108871,930811},20] (* Harvey P. Dale, Feb 04 2016 *)
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Vec(-x*(x^4+75*x^3-872*x^2+75*x+1)/((x-1)*(x^2-38*x+1)*(x^2+38*x+1)) + O(x^100))
A253579
Centered pentagonal numbers (A005891) which are also centered octagonal numbers (A016754).
Original entry on oeis.org
1, 22801, 1666681, 47411143081, 3465632747641, 98584929298781641, 7206305041398228481, 204993755756525779060081, 14984516863488437537571601, 426256225957302372068628976801, 31158234954289838149958560780201, 886340998518823181233611960679431001
Offset: 1
22801 is in the sequence because it is the 96th centered pentagonal number and the 76th centered octagonal number.
A253442
Expansion of x * (96 - 816*x) / ((1 - x) * (1 - 1442*x + x^2)) in powers of x.
Original entry on oeis.org
96, 137712, 198579888, 286352060064, 412919472031680, 595429592317621776, 858609059202538568592, 1238113667940468298287168, 1785359050561096083591526944, 2574486512795432612070683565360, 3712407766091963265509842109721456
Offset: 1
G.f. = 96*x + 137712*x^2 + 198579888*x^3 + 286352060064*x^4 + ...
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m:=20; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(48*x*(2 - 17*x)/((1 - x)*(1 - 1442*x + x^2)))); // G. C. Greubel, Aug 03 2018
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CoefficientList[Series[48*x*(2-17*x)/((1-x)*(1-1442*x+x^2)), {x,0,30}], x] (* G. C. Greubel, Aug 03 2018 *)
LinearRecurrence[{1443,-1443,1},{96,137712,198579888},20] (* Harvey P. Dale, Aug 23 2020 *)
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{a(n) = my(t=(721 - 228*quadgen(40))^n); (1 - real(t) - 4*imag(t)) / 2};
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Vec(48*x*(2 - 17*x) / ((1 - x)*(1 - 1442*x + x^2)) + O(x^20)) \\ Colin Barker, Nov 24 2017
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