A173809 a(2n+1) = 1+A131941(2n+1). a(2n) = A131941(2n).

2, 3, 9, 16, 30, 47, 73, 104, 146, 195, 257, 328, 414, 511, 625, 752, 898, 1059, 1241, 1440, 1662, 1903, 2169, 2456, 2770, 3107, 3473, 3864, 4286, 4735, 5217, 5728, 6274, 6851, 7465, 8112, 8798, 9519, 10281, 11080

Offset: 1

Author

Paul Curtz, Feb 25 2010

Keywords

• nonn
• easy

Comments

An array T(n,k) of a(n) and its successive differences is T(1,k) = a(k), T(n,k) = T(n-1,k+1)-T(n-1,k) and starts:

2, 3, 9, 16, 30, 47, 73, 104, 146, 195, 257, 328,...

1, 6, 7, 14, 17, 26, 31, 42, 49, 62, 71, 86, 97, 114,... interleaved A056220 and A051890

5, 1, 7, 3, 9, 5, 11, 7, 13, 9, 15, 11, 17, 13, 19, 15.... A158552

-4, 6, -4, 6, -4, 6, -4, 6, -4, 6, -4, 6, -4, 6, -4,... A010711

10, -10, 10, -10, 10, -10, 10, -10, 10, -10, 10,..

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-2,-2,3,-1).

Programs

Mathematica

LinearRecurrence[{3,-2,-2,3,-1},{2,3,9,16,30},60] (* Harvey P. Dale, Aug 10 2021 *)

Formula

G.f.: -x*(-2+3*x+x^3-4*x^2) / ( (1+x)*(x-1)^4 ). - R. J. Mathar, Jan 13 2011

a(2n) = A172482(n-1).

a(n)+a(n+1) = A116731(n+2). - R. J. Mathar, Jan 13 2011