A198628 - OEIS

A198628

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

1, 3, 15, 81, 435, 2313, 12195, 63801, 331395, 1710153, 8775075, 44808921, 227890755, 1155180393, 5839846755, 29458152441, 148335904515, 745888593033, 3746364947235, 18799770158361, 94271405748675, 472449569948073, 2366624981836515, 11850654345690681, 59323452211439235

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OFFSET

0,2

COMMENTS

Old name was: Alternating sums of powers for 1,2,3,4 and 5. See A196848 for the e.g.f.s and o.g.f.s of such sequences for the numbers 1,2,...,2*n+1, and A196847 for the numbers 1,2,...,2*n.

LINKS

Table of n, a(n) for n=0..24.

Index entries for linear recurrences with constant coefficients, signature (15,-85,225,-274,120).

FORMULA

a(n) = Sum_{j=1..5} j^n*(-1)^(j+1).

E.g.f.: Sum_{j=1..5} exp(j*x)*(-1)^(j+1) = exp(x)*(1+exp(5*x))/(1+exp(x)).

O.g.f.: Sum_{j=1..5} (-1)^(j+1)/(1-j*x) = (1-12*x+55*x^2-114*x^3+94*x^4)/Product_{j=1..5} (1-j*x).

A formula for the numbers of the numerator polynomial is given in A196848.

a(n) = 15*a(n-1) - 85*a(n-2) + 225*a(n-3) - 274*a(n-4) + 120*a(n-5). - Wesley Ivan Hurt, Feb 13 2026

MAPLE

A198628 := proc(n)

3^n-4^n+1-2^n+5^n ;