A263943 Positive integers n such that (n+21)^3 - n^3 is a square.

7, 119, 4564, 32900, 1161895, 8359127, 295119412, 2123188004, 74959171399, 539281396535, 19039334418580, 136975351534532, 4835915983150567, 34791200008377239, 1228303620385828084, 8836827826776286820, 311984283662017185415, 2244519476801168477687

Offset: 1

Author

Colin Barker, Oct 30 2015

Keywords

• nonn
• easy

Examples

			7 is in the sequence because (7+21)^3 - 7^3 = 147^2.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..831
• Index entries for linear recurrences with constant coefficients, signature (1,254,-254,-1,1).

Crossrefs

Cf. A263942 (4), A263944 (28), A263945 (39), A263946 (52), A263947 (57), A263948 (61), A263949 (84) where the parenthesized number is k in the expression (n+k)^3 - n^3.

Programs

Mathematica

LinearRecurrence[{1,254,-254,-1,1},{7,119,4564,32900,1161895},20] (* Harvey P. Dale, Jan 11 2017 *)

PARI

Vec(7*x*(4*x^4+16*x^3-381*x^2-16*x-1)/((x-1)*(x^2-16*x+1)*(x^2+16*x+1)) + O(x^30))

Formula

a(n) = a(n-1)+254*a(n-2)-254*a(n-3)-a(n-4)+a(n-5) for n>5.

G.f.: 7*x*(4*x^4+16*x^3-381*x^2-16*x-1) / ((x-1)*(x^2-16*x+1)*(x^2+16*x+1)).