A263622 - OEIS

%I #7 Oct 26 2015 10:16:37

%S 0,1,4,14,47,153,486,1516,4669,14255,43268,130818,394491,1187557,

%T 3570850,10728920,32219513,96724059,290303232,871171822,2614039735,

%U 7843167761,23531600414,70598995524,211805375157,635432902663,1906332262396,5719063896026,17157325905779,51472246152765

%N a(n) = (3^(n+1)-2^(n+2)+2*n+1)/4.

%H Colin Barker, <a href="/A263622/b263622.txt">Table of n, a(n) for n = 0..1000</a>

%H H. Gupta, <a href="/A002783/a002783_1.pdf">On a problem in parity</a>, Indian J. Math., 11 (1969), 157-163. [Annotated scanned copy] See Q(w) on first page.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (7,-17,17,-6).

%F From _Colin Barker_, Oct 26 2015: (Start)

%F a(n) = 7*a(n-1)-17*a(n-2)+17*a(n-3)-6*a(n-4) for n>3.

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

%F (End)

%o (PARI) a(n) = (3^(n+1)-2^(n+2)+2*n+1)/4 \\ _Colin Barker_, Oct 26 2015

%o (PARI) concat(0, Vec(x*(3*x^2-3*x+1)/((x-1)^2*(2*x-1)*(3*x-1)) + O(x^40))) \\ _Colin Barker_, Oct 26 2015

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_, Oct 23 2015

%E Typo in last term fixed by _Colin Barker_, Oct 26 2015