A210728 a(n) = a(n-1) + a(n-2) + n + 2 with n>1, a(0)=1, a(1)=2.

1, 2, 7, 14, 27, 48, 83, 140, 233, 384, 629, 1026, 1669, 2710, 4395, 7122, 11535, 18676, 30231, 48928, 79181, 128132, 207337, 335494, 542857, 878378, 1421263, 2299670, 3720963, 6020664, 9741659, 15762356, 25504049, 41266440, 66770525, 108037002, 174807565

Offset

0,2

Links

Bruno Berselli, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-2,-1,1).

Formula

G.f.: (1-x+3*x^2-2*x^3)/((1-x)^2*(1-x-x^2)). - Bruno Berselli, Jun 27 2012

a(n) = ((5+sqrt(5))*(1+sqrt(5))^(n+1)-(5-sqrt(5))*(1-sqrt(5))^(n+1))/(2^(n+1)*sqrt(5))-n-5. - Bruno Berselli, Jun 27 2012

a(n) = -n-5+A022112(n+1). R. J. Mathar, Jul 03 2012

Mathematica

RecurrenceTable[{a[0] == 1, a[1] == 2, a[n] == a[n - 1] + a[n - 2] + n + 2}, a, {n, 36}] (* Bruno Berselli, Jun 27 2012 *)
nxt[{n_, a_, b_}]:={n+1, b, a+b+n+3}; NestList[nxt, {1, 1, 2}, 40][[;; , 2]] (* Harvey P. Dale, Aug 26 2024 *)

Crossrefs

Cf. A065220: a(n)=a(n-1)+a(n-2)+n-5, a(0)=1,a(1)=2 (except first 2 terms).

Cf. A168043: a(n)=a(n-1)+a(n-2)+n-3, a(0)=1,a(1)=2 (except first 2 terms).

Cf. A131269: a(n)=a(n-1)+a(n-2)+n-2, a(0)=1,a(1)=2.

Cf. A000126: a(n)=a(n-1)+a(n-2)+n-1, a(0)=1,a(1)=2.

Cf. A104161: a(n)=a(n-1)+a(n-2)+n, a(0)=1,a(1)=2 (except the first term).

Cf. A192969: a(n)=a(n-1)+a(n-2)+n+1, a(0)=1,a(1)=2.

Cf. A210729: a(n)=a(n-1)+a(n-2)+n+3, a(0)=1,a(1)=2.

Sequence in context: A014112 A227016 A268347 * A294533 A294541 A294564

Adjacent sequences: A210725 A210726 A210727 * A210729 A210730 A210731

Keyword

nonn,easy

Author

Alex Ratushnyak, May 10 2012

Status

approved