A081351 First row in square maze array of natural numbers A081349.

1, 8, 9, 24, 25, 48, 49, 80, 81, 120, 121, 168, 169, 224, 225, 288, 289, 360, 361, 440, 441, 528, 529, 624, 625, 728, 729, 840, 841, 960, 961, 1088, 1089, 1224, 1225, 1368, 1369, 1520, 1521, 1680, 1681, 1848, 1849, 2024, 2025, 2208, 2209, 2400, 2401, 2600, 2601

Offset

0,2

Comments

Interleaves the odd squares A016754 with 8 times the triangular numbers A000217.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

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

Formula

a(n) = (n+1)*(n+2)-(n+1)*(-1)^n = 2*C(n+2,2)-C(n+1,1)*(-1)^n.

G.f.: (x^3-x^2+7*x+1)/((1-x)^3*(1+x)^2). - Colin Barker, Sep 03 2012

From Amiram Eldar, Feb 03 2026: (Start)

Sum_{n>=0} 1/a(n) = Pi^2/8 + 1/4.

Sum_{n>=0} (-1)^n/a(n) = Pi^2/8 - 1/4. (End)

Mathematica

a[n_] := (n+1)*(n+2-(-1)^n); Array[a, 50, 0] (* Amiram Eldar, Feb 03 2026 *)

Prog

(Magma) [(n+1)*(n+2)-(n+1)*(-1)^n: n in [0..50]]; // Vincenzo Librandi, Sep 06 2011

Crossrefs

Cf. A000217, A016754, A081350, A081352.

Sequence in context: A278076 A394855 A389100 * A032462 A077599 A109097

Adjacent sequences: A081348 A081349 A081350 * A081352 A081353 A081354

Keyword

nonn,easy

Author

Paul Barry, Mar 19 2003

Status

approved