A258442
9-gonal numbers (A001106) that are the sum of eight consecutive 9-gonal numbers.
Original entry on oeis.org
2484, 3706711688304, 5696462668411740751524, 8754305611527549602378580888144, 13453588867526192558135312033676410914164, 20675432347037054365824241005098474993236683565584, 31773938310893899311445242803186409506547794898889170298404
Offset: 1
2484 is in the sequence because A001106(27) = 2484 = 111 + 154 + 204 + 261 + 325 + 396 + 474 + 559 = A001106(6) + ... + A001106(13).
A258443
9-gonal numbers (A001106) that are the sum of eleven consecutive 9-gonal numbers.
Original entry on oeis.org
10039491, 9002622519, 632913667646139, 567557703066557511, 39901154831776816303176, 35780879673931397997716604, 2515512364950294599811639195654, 2255755394249701567388335466918226, 158586950299955622830941025383070794461
Offset: 1
10039491 is in the sequence because A001106(1694) = 10039491 = 894861 + 898404 + 901954 + 905511 + 909075 + 912646 + 916224 + 919809 + 923401 + 927000 + 930606 = A001106(506) + ... + A001106(516).
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LinearRecurrence[{1,63043598,-63043598,-1,1},{10039491,9002622519,632913667646139,567557703066557511,39901154831776816303176},10] (* Harvey P. Dale, Jan 10 2019 *)
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Vec(-99*x*(4*x^4+572*x^3-211815202*x^2+90834172*x+101409) / ((x-1)*(x^2-7940*x+1)*(x^2+7940*x+1)) + O(x^20))
A258444
9-gonal numbers (A001106) that are the sum of twelve consecutive 9-gonal numbers.
Original entry on oeis.org
1349094322576, 1910746510353532612000, 2706224588156555124000697809136, 3832874471762384783002138104903925699456, 5428568929785331587316097630206410288870519307600, 7688579639781530489126233275115806835015504771403279234656
Offset: 1
1349094322576 is in the sequence because A001106(620851) = 1349094322576 = 112417626816 + 112418881350 + 112420135891 + 112421390439 + 112422644994 + 112423899556 + 112425154125 + 112426408701 + 112427663284 + 112428917874 + 112430172471 + 112431427075 = A001106(179219) + ... + A001106(179230).
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I:=[1349094322576,1910746510353532612000, 2706224588156555124000697809136]; [n le 3 select I[n] else 1416317955*Self(n-1)-1416317955*Self(n-2)+Self(n-3): n in [1..10]]; // Vincenzo Librandi, May 31 2015
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CoefficientList[Series[16 (76 x^2 - 106213627505 x + 84318395161)/((1 - x) (x^2 - 1416317954 x + 1)), {x, 0, 33}], x] (* Vincenzo Librandi, May 31 2015 *)
LinearRecurrence[{1416317955,-1416317955,1},{1349094322576,1910746510353532612000,2706224588156555124000697809136},10] (* Harvey P. Dale, Jan 19 2016 *)
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Vec(-16*x*(76*x^2-106213627505*x+84318395161) / ((x-1)*(x^2-1416317954*x+1)) + O(x^20))
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