cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Views

Author

Colin Barker, May 30 2015

Keywords

Examples

			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.
		

Crossrefs

Programs

  • PARI
    Vec(-x*(x^2-32537*x+24486)/((x-1)*(x^2-39202*x+1)) + O(x^20))

Formula

a(n) = 39203*a(n-1) - 39203*a(n-2) + a(n-3).
G.f.: -x*(x^2-32537*x+24486) / ((x-1)*(x^2-39202*x+1)).
a(n) = (46+(89-36*sqrt(2))*(19601+13860*sqrt(2))^(-n)+(89+36*sqrt(2))*(19601+13860*sqrt(2))^n)/224. - Colin Barker, Mar 07 2016

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

Views

Author

Colin Barker, May 30 2015

Keywords

Examples

			2484 is in the sequence because A001106(27) = 2484 = 111 + 154 + 204 + 261 + 325 + 396 + 474 + 559 = A001106(6) + ... + A001106(13).
		

Crossrefs

Programs

  • PARI
    Vec(-36*x*(22897724*x^2-3074765843*x+69) / ((x-1)*(x^2-1536796802*x+1)) + O(x^20))

Formula

a(n) = 1536796803*a(n-1) - 1536796803*a(n-2) + a(n-3).
G.f.: -36*x*(22897724*x^2-3074765843*x+69) / ((x-1)*(x^2-1536796802*x+1)).
a(n) = (16014+(92323615161-65282654344*sqrt(2))*(768398401+543339720*sqrt(2))^n+(768398401+543339720*sqrt(2))^(-n)*(92323615161+65282654344*sqrt(2)))/224. - Colin Barker, Mar 07 2016

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

Views

Author

Colin Barker, May 30 2015

Keywords

Examples

			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).
		

Crossrefs

Programs

  • Magma
    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
  • Mathematica
    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 *)
  • PARI
    Vec(-16*x*(76*x^2-106213627505*x+84318395161) / ((x-1)*(x^2-1416317954*x+1)) + O(x^20))
    

Formula

a(n) = 1416317955*a(n-1) - 1416317955*a(n-2) + a(n-3).
G.f.: -16*x*(76*x^2-106213627505*x+84318395161) / ((x-1)*(x^2-1416317954*x+1)).
a(n) = (55406+2523*(708158977+408855776*sqrt(3))^(-n)*(43-24*sqrt(3)+(43+24*sqrt(3))*(708158977+408855776*sqrt(3))^(2*n)))/224. - Colin Barker, Mar 07 2016
Showing 1-3 of 3 results.