A190716 a(2*n) = 2*n and a(2*n-1) = A054569(n).

1, 2, 7, 4, 21, 6, 43, 8, 73, 10, 111, 12, 157, 14, 211, 16, 273, 18, 343, 20, 421, 22, 507, 24, 601, 26, 703, 28, 813, 30, 931, 32, 1057, 34, 1191, 36, 1333, 38, 1483, 40, 1641, 42, 1807, 44, 1981, 46, 2163, 48, 2353, 50, 2551, 52, 2757, 54, 2971, 56, 3193

Offset: 1

Author

Johannes W. Meijer, May 18 2011

Keywords

• nonn
• easy

Comments

Equals the Row2 triangle sums of the Connell sequence A001614 as a triangle. The Row2(n) triangle sums are defined by Row2(n) = sum((-1)^(n+k)*T(n,k), k=1..n), see A180662.

Links

• Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).

Crossrefs

Cf. A001614, A054569, A180662.

Programs

Maple

A190716:= n-> coeff (series (x*(1+2*x+4*x^2-2*x^3+3*x^4)/(1-x^2)^3, x, n+1), x, n): seq(A190716(n), n=1..49);

Mathematica

a[n_]:=(1-(-1)^n(n-1)^2+n^2)/2; Array[a,57] (* Stefano Spezia, Aug 19 2025 *)

Formula

a(2*n) = 2*n and a(2*n-1) = 4*n^2 - 6*n + 3.

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

From Stefano Spezia, Aug 19 2025: (Start)

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

E.g.f.: (1 + x + x^2)*sinh(x). (End)