login
A258128
Octagonal numbers (A000567) that are the sum of two consecutive octagonal numbers.
5
5461, 813281, 7272157205, 1083057360705, 9684433559760981, 1442322650052752161, 12896895753596262561301, 1920761265591267733640321, 17174976631595008767000306005, 2557904668044167195987033355105, 22872156829955018609383449248248341
OFFSET
1,1
FORMULA
G.f.: -x*(x^4+20*x^3-1146230*x^2+807820*x+5461) / ((x-1)*(x^2-1154*x+1)*(x^2+1154*x+1)).
EXAMPLE
5461 is in the sequence because Oct(43) = 5461 = 2640 + 2821 = Oct(30) + Oct(31).
MATHEMATICA
CoefficientList[Series[-x*(x^4 +20*x^3 -1146230*x^2 +807820*x +5461)/((x-1)*(x^2 -1154*x +1)*(x^2 +1154*x +1)), {x, 0, 50}], x] (* G. C. Greubel, Oct 18 2017 *)
LinearRecurrence[{1, 1331714, -1331714, -1, 1}, {5461, 813281, 7272157205, 1083057360705, 9684433559760981}, 20] (* Harvey P. Dale, Feb 19 2018 *)
PROG
(PARI) Vec(-x*(x^4 +20*x^3 -1146230*x^2 +807820*x +5461)/((x-1)*(x^2 -1154*x +1)*(x^2 +1154*x +1)) + O('x^20))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, May 21 2015
STATUS
approved