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A252747 Numbers n such that the hexagonal number H(n) is equal to the sum of four consecutive squares. 2
18, 42, 602, 1418, 20442, 48162, 694418, 1636082, 23589762, 55578618, 801357482, 1888036922, 27222564618, 64137676722, 924765839522, 2178792971618, 31414815979122, 74014823358282, 1067178977450618, 2514325201209962, 36252670417341882, 85413042017780418 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Also positive integers y in the solutions to 8*x^2-4*y^2+24*x+2*y+28 = 0, the corresponding values of x being A201633.
LINKS
FORMULA
a(n) = a(n-1)+34*a(n-2)-34*a(n-3)-a(n-4)+a(n-5).
G.f.: -2*x*(x^4-26*x^2+12*x+9) / ((x-1)*(x^2-6*x+1)*(x^2+6*x+1)).
EXAMPLE
18 is in the sequence because H(18) = 630 = 121+144+169+196 = 11^2+12^2+13^2+14^2.
PROG
(PARI) Vec(-2*x*(x^4-26*x^2+12*x+9)/((x-1)*(x^2-6*x+1)*(x^2+6*x+1)) + O(x^100))
CROSSREFS
Sequence in context: A144737 A333457 A304152 * A067750 A043362 A023735
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Dec 21 2014
STATUS
approved

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Last modified February 25 06:40 EST 2024. Contains 370310 sequences. (Running on oeis4.)