A008609 a(n) = n + max_{0 <= i <n} ((n-i)*a(i)), a(0) = 1.

1, 2, 4, 7, 12, 19, 30, 45, 68, 99, 146, 215, 309, 451, 659, 942, 1369, 1994, 2844, 4126, 6002, 8553, 12400, 18029, 25683, 37225, 54113, 77076, 111703, 162368, 231258, 335140, 487136, 693807, 1005454, 1461443, 2081457, 3016399

Offset

0,2

Links

Robert Israel, Table of n, a(n) for n = 0..6277

Formula

G.f.: (1+x^2-2*x^3+2*x^4-x^5+x^6-2*x^7+2*x^8-4*x^9+4*x^10-2*x^11+x^12)/(1-3*x^3)/(1-x)^2. - Vladeta Jovovic, Mar 23 2003

a(n+3) = 3*a(n) + n + 3 for n >= 8. - Robert Israel, Mar 28 2018

Maple

f:= gfun:-rectoproc({a(n+3)=3*a(n)+n+3, seq(a(i)=[1, 2, 4, 7, 12, 19, 30, 45, 68, 99, 146][i+1], i=0..10)}, a(n), remember):
map(f, [$0..50]); # Robert Israel, Mar 28 2018

Crossrefs

Cf. A000792.

Sequence in context: A347547 A000070 A369579 * A264392 A100823 A102346

Adjacent sequences: A008606 A008607 A008608 * A008610 A008611 A008612

Keyword

easy,nonn

Author

Mark Herbster (mark(AT)cse.ucsc.edu)

Status

approved