A105037 a(n) = 22*a(n-2) - a(n-4) + 10, for n > 3, with a(0) = 0, a(1) = 4, a(2) = 6, a(3) = 98.

0, 4, 6, 98, 142, 2162, 3128, 47476, 68684, 1042320, 1507930, 22883574, 33105786, 502396318, 726819372, 11029835432, 15956920408, 242153983196, 350325429614, 5316357794890, 7691202531110, 116717717504394, 168856130254816

Offset: 0

Author

Gerald McGarvey, Apr 03 2005

Keywords

• nonn
• easy

Comments

It appears this sequence gives all nonnegative m such that 120*m^2 + 120*m + 1 is a square.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,22,-22,-1,1).

Crossrefs

Cf. A077421.

Programs

Magma

R:=PowerSeriesRing(Integers(), 40); [0] cat Coefficients(R!( 2*x*(2+x+2*x^2)/((1-x)*(1-22*x^2+x^4)) )); // G. C. Greubel, Mar 14 2023

Mathematica

LinearRecurrence[{1,22,-22,-1,1}, {0,4,6,98,142}, 41] (* G. C. Greubel, Mar 14 2023 *)

SageMath

@CachedFunction
def a(n): # a = A105037
    if (n<5): return (0,4,6,98,142)[n]
    else: return a(n-1) +22*a(n-2) -22*a(n-3) -a(n-4) +a(n-5)
[a(n) for n in range(41)] # G. C. Greubel, Mar 14 2023

Formula

a(n) = 22*a(n-2) - a(n-4) + 10, for n > 3.

G.f.: 2*x*(2 + x + 2*x^2)/((1-x)*(1-22*x^2+x^4)). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009