A304578 a(n) = (n^2 + 1) * 5^n + (n^2 + 2) * 3^n.

3, 19, 179, 1547, 12083, 87811, 605827, 4017787, 25823651, 161789939, 992351123, 5978820331, 35477981011, 207792160483, 1203339605987, 6900229858139, 39226193944643, 221290021193683, 1239902910407539, 6905023951693771, 38243741775219827, 210766657862250179, 1156345359837548099

Offset: 0

Author

Vincenzo Librandi, May 16 2018

Keywords

• nonn
• easy

Links

• Daniele Mastrostefano and Carlo Sanna, On numbers n with polynomial image coprime with the nth term of a linear recurrence, arXiv:1805.05114 [math.NT], 2018 (see 4.2, page 7).
• Index entries for linear recurrences with constant coefficients, signature (24,-237,1232,-3555,5400,-3375).

Programs

Magma

[(n^2+1)*5^n+(n^2+2)*3^n: n in [0..25]];

Mathematica

CoefficientList[Series[(3 - 53 x + 434 x^2 - 1942 x^3 + 4635 x^4 - 4725 x^5)/((1-5 x)^3(1-3 x)^3), {x, 0, 33}], x] (* or *) Table[(n^2 + 1) 5^n + (n^2 + 2) 3^n, {n, 0, 20}]

PARI

a(n)=(n^2+1)*5^n+(n^2+2)*3^n \\ Charles R Greathouse IV, May 16 2018

Formula

G.f.: (3-53*x+434*x^2-1942*x^3+4635*x^4-4725*x^5)/((1-5*x)^3(1-3*x)^3).