A252747 Numbers n such that the hexagonal number H(n) is equal to the sum of four consecutive squares.

18, 42, 602, 1418, 20442, 48162, 694418, 1636082, 23589762, 55578618, 801357482, 1888036922, 27222564618, 64137676722, 924765839522, 2178792971618, 31414815979122, 74014823358282, 1067178977450618, 2514325201209962, 36252670417341882, 85413042017780418

Offset: 1

Author

Colin Barker, Dec 21 2014

Keywords

• nonn
• easy

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.

Examples

			18 is in the sequence because H(18) = 630 = 121+144+169+196 = 11^2+12^2+13^2+14^2.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,34,-34,-1,1).

Crossrefs

Cf. A000290, A000384, A201633,

Programs

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))

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)).