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

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

Views

Author

Colin Barker, May 30 2015

Keywords

Examples

			10039491 is in the sequence because A001106(1694) = 10039491 = 894861 + 898404 + 901954 + 905511 + 909075 + 912646 + 916224 + 919809 + 923401 + 927000 + 930606 = A001106(506) + ... + A001106(516).
		

Crossrefs

Programs

  • Mathematica
    LinearRecurrence[{1,63043598,-63043598,-1,1},{10039491,9002622519,632913667646139,567557703066557511,39901154831776816303176},10] (* Harvey P. Dale, Jan 10 2019 *)
  • PARI
    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))

Formula

a(n) = a(n-1) + 63043598*a(n-2) - 63043598*a(n-3) - a(n-4) + a(n-5).
G.f.: -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)).
Showing 1-3 of 3 results.