A070315 Third diagonal of triangle in A046739.

1, 21, 161, 813, 3361, 12421, 42865, 141549, 453905, 1426725, 4422913, 13579309, 41408833, 125667333, 380081105, 1146795693, 3454279345, 10392196645, 31238454241, 93845384301, 281808780641, 845996765061, 2539181475121, 7620027450733, 22865249731921

Offset

4,2

Links

Table of n, a(n) for n=4..28.

D. P. Roselle, Permutations by number of rises and successions, Proc. Amer. Math. Soc., 19 (1968), 8-16.

D. P. Roselle, Permutations by number of rises and successions, Proc. Amer. Math. Soc., 19 (1968), 8-16. [Annotated scanned copy]

Index entries for linear recurrences with constant coefficients, signature (10,-40,82,-91,52,-12).

Formula

a(n) = 3^n - (3n+2)*2^(n-1) + 2n^2. - Ralf Stephan, May 09 2004

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]

Prog

(PARI) a(n) = 3^n - (3*n+2)*2^(n-1) + 2*n^2; \\ Michel Marcus, Oct 25 2017

Crossrefs

Cf. A046739.

Sequence in context: A296832 A267473 A179097 * A242191 A146301 A338891

Adjacent sequences: A070312 A070313 A070314 * A070316 A070317 A070318

Keyword

nonn,easy

Author

N. J. A. Sloane, May 15 2002

Extensions

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

More terms from Colin Barker, Feb 03 2013

Status

approved