A334991 a(n) = 4^n + 3 * 18^n.

4, 58, 988, 17560, 315184, 5669728, 102040768, 1836676480, 33059947264, 595078133248, 10711402728448, 192805234432000, 3470494161055744, 62468894664122368, 1124440103014678528, 20239921850506117120, 364318593294077722624, 6557734679233269465088, 118039224225958332203008

Offset

0,1

Comments

This sequence is a variation of the sequence A333385, variation proposed by Tony Gardiner in his book in reference.

Proposition: a(n) is a perfect square iff n = 0; in this case, a(0) = 4.

References

A. Gardiner, The Mathematical Olympiad Handbook: An Introduction to Problem Solving, Oxford University Press, 1997, reprinted 2011, page 115 (1991).

Links

Table of n, a(n) for n=0..18.

Index entries for linear recurrences with constant coefficients, signature (22,-72).

Formula

a(n) = A000302(n) + 3 * A001027(n).

a(n) = 22*a(n-1) - 72*a(n-2) for n>1.

G.f.: (4 - 30*x)/((1 - 4*x)*(1 - 18*x)). - Alejandro J. Becerra Jr., Jun 01 2020

Example

a(4) = 4^4 + 3 * 18^4 = 315184 = 2^4 * 19699 is not a perfect square.

Maple

S:=seq(4^n+3*18^n, n=0..20);

Crossrefs

Cf. A000302, A001027, A333385.

Sequence in context: A197177 A155668 A240430 * A216795 A216352 A295406

Adjacent sequences: A334988 A334989 A334990 * A334992 A334993 A334994

Keyword

nonn,easy

Author

Bernard Schott, May 18 2020

Status

approved