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

Author

N. J. A. Sloane, May 15 2002

Keywords

• nonn
• easy

Links

• 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).

Crossrefs

Cf. A046739.

Programs

PARI

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

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]

Extensions

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

More terms from Colin Barker, Feb 03 2013