A070315 - OEIS

%I #16 Oct 25 2017 06:01:54

%S 1,21,161,813,3361,12421,42865,141549,453905,1426725,4422913,13579309,

%T 41408833,125667333,380081105,1146795693,3454279345,10392196645,

%U 31238454241,93845384301,281808780641,845996765061,2539181475121,7620027450733,22865249731921

%N Third diagonal of triangle in A046739.

%H D. P. Roselle, <a href="http://dx.doi.org/10.1090/S0002-9939-1968-0218256-9">Permutations by number of rises and successions</a>, Proc. Amer. Math. Soc., 19 (1968), 8-16.

%H D. P. Roselle, <a href="/A046739/a046739.pdf"> Permutations by number of rises and successions</a>, Proc. Amer. Math. Soc., 19 (1968), 8-16. [Annotated scanned copy]

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (10,-40,82,-91,52,-12).

%F a(n) = 3^n - (3n+2)*2^(n-1) + 2n^2. - _Ralf Stephan_, May 09 2004

%F G.f.: -x^4*(12*x^5-40*x^4+39*x^3+9*x^2-11*x-1) / ((x-1)^3*(2*x-1)^2*(3*x-1)). [_Colin Barker_, Feb 03 2013]

%o (PARI) a(n) = 3^n - (3*n+2)*2^(n-1) + 2*n^2; \\ _Michel Marcus_, Oct 25 2017

%Y Cf. A046739.

%K nonn,easy

%O 4,2

%A _N. J. A. Sloane_, May 15 2002

%E More terms from Larry Reeves (larryr(AT)acm.org), Oct 01 2002

%E More terms from _Colin Barker_, Feb 03 2013