A258441
9-gonal numbers (A001106) that are the sum of two consecutive 9-gonal numbers.
Original entry on oeis.org
24486, 959892121, 37629690894906, 1475159141502204841, 57829188627539743273926, 2267019851101653874322234161, 88871712145057846553640480297546, 3483948857243537849494160234302156081, 136577763012789458630812222951472642381766
Offset: 1
24486 is in the sequence because A001106(84) = 24486 = 12036 + 12450 = A001106(59) + A001106(60), where A001106(k) is the k-th 9-gonal number.
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).
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))
Showing 1-3 of 3 results.