A167385 - OEIS

%I #4 Nov 06 2025 09:17:11

%S 1,3,5,8,12,17,24,33,45,61,82,110,147,196,261,347,461,612,812,1077,

%T 1428,1893,2509,3325,4406,5838,7735,10248,13577,17987,23829,31568,

%U 41820,55401,73392,97225,128797,170621,226026,299422,396651,525452,696077,922107,1221533

%N a(n)= sum_{i=7..n+6} A000931(i).

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,-1).

%F a(n+1)/a(n)-> A060005 as n->infinity.

%F G.f.: (1+x)^2/((x-1)*(x^3+x^2-1)). a(n)= +a(n-1) +a(n-2) -a(n-4). [Nov 05 2009]

%F a(n) = A000931(n+12)-4. [Nov 05 2009]

%F a(n) -a(n-2)-a(n-3)-4=0. - _R. J. Mathar_, Nov 06 2025

%t Clear[f, g, n]

%t f[0] = 0; f[1] = 1; f[2] = 1; f[n_] := f[n] = f[n - 2] + f[n - 3];

%t g[n_] := Sum[f[i + 3], {i, 0, n}]

%t Table[g[n], {n, 0, 30}]

%Y Cf. A018917.

%K nonn,easy

%O 0,2

%A _Roger L. Bagula_, Nov 02 2009

%E Notation normalized, definition corrected, g.f. added - The Assoc. Editors of the OEIS, Nov 05 2009