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A253168
Numbers n such that the octagonal number O(n) is equal to the sum of the pentagonal numbers P(m), P(m+1), P(m+2) and P(m+3) for some m.
2
4, 1234, 4020, 1423650, 4638692, 1642890482, 5353046164, 1895894192194, 6177410634180, 2187860254901010, 7128726518797172, 2524788838261572962, 8226544225281301924, 2913604131493600296754, 9493424907248103622740, 3362296642954776480880770
OFFSET
1,1
COMMENTS
Also positive integers y in the solutions to 12*x^2-6*y^2+32*x+4*y+36 = 0, the corresponding values of x being A253167.
FORMULA
a(n) = a(n-1)+1154*a(n-2)-1154*a(n-3)-a(n-4)+a(n-5).
G.f.: -2*(x^4+105*x^3-915*x^2+615*x+2) / ((x-1)*(x^2-34*x+1)*(x^2+34*x+1)).
EXAMPLE
4 is in the sequence because O(4) = 40 = 1+5+12+22 = P(1)+P(2)+P(3)+P(4).
MATHEMATICA
LinearRecurrence[{1, 1154, -1154, -1, 1}, {4, 1234, 4020, 1423650, 4638692}, 20] (* Harvey P. Dale, Sep 06 2023 *)
PROG
(PARI) Vec(-2*(x^4+105*x^3-915*x^2+615*x+2)/((x-1)*(x^2-34*x+1)*(x^2+34*x+1)) + O(x^100))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Dec 29 2014
STATUS
approved