A087405 First differences of A087404: a(n) = A087404(n) - A087404(n-1), a(0) = A087404(0).

2, 2, 22, 98, 502, 2498, 12502, 62498, 312502, 1562498, 7812502, 39062498, 195312502, 976562498, 4882812502, 24414062498, 122070312502, 610351562498, 3051757812502, 15258789062498, 76293945312502, 381469726562498, 1907348632812502, 9536743164062498

Offset: 0

Author

Mario Catalani (mario.catalani(AT)unito.it), Sep 01 2003

Keywords

• easy
• nonn
• changed

Links

• Index entries for linear recurrences with constant coefficients, signature (4,5).

Programs

Mathematica

CoefficientList[Series[((1 - x)(2 - 4x))/(1 - 4x - 5x^2), {x, 0, 25}], x]
LinearRecurrence[{4,5},{2,2,22},30] (* Harvey P. Dale, Oct 23 2024 *)

Formula

G.f.: ((1-x)(2-4x))/(1-4x-5x^2).

a(n) = 4*5^(n-1)+2(-1)^n for n > 0.

E.g.f.: 2*(5*cosh(x) + 2*cosh(5*x) - 5*sinh(x) + 2*sinh(5*x) - 2)/5. - Stefano Spezia, Aug 29 2025