A252004 Numbers n such that the sum of the pentagonal numbers P(n) and P(n+1) is equal to the sum of the octagonal numbers N(m) and N(m+1) for some m.

328, 378896, 437246040, 504581551648, 582286673356136, 671958316471429680, 775439314921356494968, 894856297460928923763776, 1032663391830597056666902920, 1191692659316211542464682206288, 1375212296187516289407186599153816

Offset

1,1

Comments

Also nonnegative integers y in the solutions to 6*x^2-3*y^2+2*x-2*y = 0, the corresponding values of x being A252003.

Links

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

Index entries for linear recurrences with constant coefficients, signature (1155,-1155,1).

Formula

a(n) = 1155*a(n-1)-1155*a(n-2)+a(n-3).

G.f.: -8*x*(7*x+41) / ((x-1)*(x^2-1154*x+1)).

a(n) = (-4 - (sqrt(2)-2)*(577+408*sqrt(2))^(-n) + (sqrt(2)+2)*(577+408*sqrt(2))^n) / 12. - Colin Barker, May 30 2017

Example

328 is in the sequence because P(328)+P(329) = 161212+162197 = 323409 = 161008+162401 = N(232)+N(233).

Mathematica

LinearRecurrence[{1155, -1155, 1}, {328, 378896, 437246040}, 30] (* Harvey P. Dale, Feb 21 2017 *)

Prog

(PARI) Vec(-8*x*(7*x+41)/((x-1)*(x^2-1154*x+1)) + O(x^100))

Crossrefs

Cf. A000326, A000567, A252003.

Sequence in context: A232140 A231130 A289340 * A278352 A246858 A253054

Adjacent sequences: A252001 A252002 A252003 * A252005 A252006 A252007

Keyword

nonn,easy

Author

Colin Barker, Dec 12 2014

Status

approved