A122997 Pentanacci numbers for following initial values: a(0) = 1, a(1) = -1, a(2) = 1, a(3) = -1, a(4) = 1.

1, -1, 1, -1, 1, 1, 1, 3, 5, 11, 21, 41, 81, 159, 313, 615, 1209, 2377, 4673, 9187, 18061, 35507, 69805, 137233, 269793, 530399, 1042737, 2049967, 4030129, 7923025, 15576257, 30622115, 60201493, 118353019, 232675909, 457428793, 899281329, 1767940543, 3475679593, 6833006167, 13433336425

Offset: 0

Author

Artur Jasinski, Oct 28 2006

Keywords

• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,1,1,1).

Crossrefs

Cf. A001591.

Programs

Magma

[n le 5 select (-1)^(n-1) else Self(n-1) +Self(n-2) +Self(n-3) +Self(n-4) +Self(n-5): n in [1..51]]; // G. C. Greubel, Dec 23 2021

Mathematica

a[n_]:= a[n]= If[n<5, (-1)^n, Sum[a[n-j], {j, 5}]];
Table[a[n], {n, 0, 50}]

Sage

@CachedFunction
def A122997(n): return (-1)^n if (n<5) else sum( A122997(n-j) for j in (1..5) )
[A122997(n) for n in (0..50)] # G. C. Greubel, Dec 23 2021

Formula

a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5).

G.f.: (1 -2*x +x^2 -2*x^3 +x^4)/(1 -x -x^2 -x^3 -x^4 -x^5). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 12 2009