A258128 Octagonal numbers (A000567) that are the sum of two consecutive octagonal numbers.

5461, 813281, 7272157205, 1083057360705, 9684433559760981, 1442322650052752161, 12896895753596262561301, 1920761265591267733640321, 17174976631595008767000306005, 2557904668044167195987033355105, 22872156829955018609383449248248341

Offset

1,1

Links

Colin Barker, Table of n, a(n) for n = 1..326

Index entries for linear recurrences with constant coefficients, signature (1,1331714,-1331714,-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

Cf. A000567, A258129, A258130, A258131, A258132.

Sequence in context: A104111 A028548 A069311 * A022205 A255193 A231269

Adjacent sequences: A258125 A258126 A258127 * A258129 A258130 A258131

Keyword

nonn,easy

Author

Colin Barker, May 21 2015

Status

approved