A253167 Numbers n such that the sum of the pentagonal numbers P(n), P(n+1), P(n+2) and P(n+3) is equal to the octagonal number O(m) for some m.

1, 871, 2841, 1006671, 3280049, 1161698999, 3785175241, 1340599639711, 4368088949601, 1547050822529031, 5040770862665849, 1785295308598863599, 5817045207427441681, 2060229239072266065751, 6712865128600405035561, 2377502756594086441014591

Offset

1,2

Comments

Also positive integers x in the solutions to 12*x^2-6*y^2+32*x+4*y+36 = 0, the corresponding values of y being A253168.

Links

Colin Barker, Table of n, a(n) for n = 1..653

Index entries for linear recurrences with constant coefficients, signature (1,1154,-1154,-1,1).

Formula

a(n) = a(n-1)+1154*a(n-2)-1154*a(n-3)-a(n-4)+a(n-5).

G.f.: x*(x^4+150*x^3-816*x^2-870*x-1) / ((x-1)*(x^2-34*x+1)*(x^2+34*x+1)).

Example

1 is in the sequence because P(1)+P(2)+P(3)+P(4) = 1+5+12+22 = 40 = O(4).

Prog

(PARI) Vec(x*(x^4+150*x^3-816*x^2-870*x-1)/((x-1)*(x^2-34*x+1)*(x^2+34*x+1)) + O(x^100))

Crossrefs

Cf. A000326, A000567, A253168.

Sequence in context: A035855 A317806 A031783 * A214285 A251841 A251085

Adjacent sequences: A253164 A253165 A253166 * A253168 A253169 A253170

Keyword

nonn,easy

Author

Colin Barker, Dec 29 2014

Status

approved