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A252093
Numbers n such that the pentagonal number P(n) is equal to the sum of the octagonal numbers N(m), N(m+1) and N(m+2) for some m.
2
90, 84515202, 79520184374490, 74820382437504220002, 70398348194603325406910490, 66237665019531059286273761843202, 62322886541476336272141806645338008090, 58639479301035764180766150529698967373864802, 55173768795323625559613033164820557197489306307290
OFFSET
1,1
COMMENTS
Also nonnegative integers y in the solutions to 18*x^2-3*y^2+24*x+y+18 = 0, the corresponding values of x being A252092.
FORMULA
a(n) = 940899*a(n-1)-940899*a(n-2)+a(n-3).
G.f.: -18*x*(489*x^2-9206*x+5) / ((x-1)*(x^2-940898*x+1)).
EXAMPLE
90 is in the sequence because P(90) = 12105 = 3816+4033+4256 = N(36)+N(37)+N(38).
PROG
(PARI) Vec(-18*x*(489*x^2-9206*x+5)/((x-1)*(x^2-940898*x+1)) + O(x^100))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Dec 14 2014
STATUS
approved