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

0,2

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

Table of n, a(n) for n=0..47.

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

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

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 *)

Prog

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

Crossrefs

Cf. A083362.

Sequence in context: A153325 A109907 A121534 * A027707 A046861 A078917

Adjacent sequences: A083360 A083361 A083362 * A083364 A083365 A083366

Keyword

nonn,easy

Author

Paul D. Hanna, Apr 27 2003

Status

approved