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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. 2
1, 871, 2841, 1006671, 3280049, 1161698999, 3785175241, 1340599639711, 4368088949601, 1547050822529031, 5040770862665849, 1785295308598863599, 5817045207427441681, 2060229239072266065751, 6712865128600405035561, 2377502756594086441014591 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 6 19:30 EST 2021. Contains 349567 sequences. (Running on oeis4.)