A276764 1^2 + 3^2, 2^2 + 4^2, 5^2 + 7^2, 6^2 + 8^2, ...

10, 20, 74, 100, 202, 244, 394, 452, 650, 724, 970, 1060, 1354, 1460, 1802, 1924, 2314, 2452, 2890, 3044, 3530, 3700, 4234, 4420, 5002, 5204, 5834, 6052, 6730, 6964, 7690, 7940, 8714, 8980, 9802, 10084, 10954, 11252, 12170, 12484, 13450, 13780, 14794, 15140

Offset: 1

Author

Edwin McCravy, Nov 06 2016

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Quora, What is the next number in this sequence: 10, 20, 74, 100?
• Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Crossrefs

Cf. A001844.

Programs

Mathematica

LinearRecurrence[{1,2,-2,-1,1},{10,20,74,100,202},50] (* Harvey P. Dale, Mar 02 2023 *)

PARI

Vec(2*x*(5+5*x+17*x^2+3*x^3+2*x^4) / ((1-x)^3*(1+x)^2) + O(x^60)) \\ Colin Barker, Nov 10 2016

Formula

a(n) = (2n - 1 - ((n+1) mod 2))^2 + (2n + (n mod 2))^2.

From Colin Barker, Nov 10 2016: (Start)

G.f.: 2*x*(5 + 5*x + 17*x^2 + 3*x^3 + 2*x^4) / ((1 - x)^3 * (1 + x)^2).

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

a(n) = 8*n^2 - 8*n + 4 for n even.

a(n) = 8*n^2 + 2 for n odd.

(End)