A083363 Diagonal of table A083362.

1, 7, 11, 30, 38, 69, 81, 124, 140, 195, 215, 282, 306, 385, 413, 504, 536, 639, 675, 790, 830, 957, 1001, 1140, 1188, 1339, 1391, 1554, 1610, 1785, 1845, 2032, 2096, 2295, 2363, 2574, 2646, 2869, 2945, 3180, 3260, 3507, 3591, 3850, 3938, 4209, 4301, 4584

Offset: 0

Author

Paul D. Hanna, Apr 27 2003

Keywords

• nonn
• easy

Comments

A083362 is the square table of least distinct positive integers such that the sum of any two consecutive terms in any row form a square.

Links

• Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Crossrefs

Cf. A083362.

Programs

Magma

[(4*n+3)*(2*n+1-(-1)^n)/4+0^n : n in [0..50]]; // Wesley Ivan Hurt, Sep 26 2014

Maple

A083363:=n->(4*n+3)*(2*n+1-(-1)^n)/4+0^n: seq(A083363(n), n=0..50); # Wesley Ivan Hurt, Sep 26 2014

Mathematica

Join[{1}, Table[(4 n + 3) (2 n + 1 - (-1)^n)/4, {n, 30}]] (* Wesley Ivan Hurt, Sep 26 2014 *)
LinearRecurrence[{1,2,-2,-1,1},{1,7,11,30,38,69},50] (* Harvey P. Dale, Oct 04 2023 *)

PARI

Vec((x^5-x^4-7*x^3-2*x^2-6*x-1)/((x-1)^3*(x+1)^2) + O(x^100)) \\ Colin Barker, Sep 26 2014

Formula

a(0) = 1; a(2n-1) = 8n^2 - n (n>0); a(2n) = 8n^2 + 3n (n>0).

a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5). - Colin Barker, Sep 26 2014

G.f.: (x^5-x^4-7*x^3-2*x^2-6*x-1) / ((x-1)^3*(x+1)^2). - Colin Barker, Sep 26 2014

a(n) = (4n+3)*(2n+1-(-1)^n)/4+0^n. - Wesley Ivan Hurt, Sep 26 2014