OFFSET
1,1
LINKS
Index entries for linear recurrences with constant coefficients, signature (7,-11,5).
FORMULA
G.f.: x * (4 - 5*x)/((1 - x)^2 * (1 - 5*x)).
a(n) = 7*a(n-1) - 11*a(n-2) + 5*a(n-3).
a(n) = 3*A014827(n) + n.
a(n) = (3*5^(n+1) + 4*n - 15)/16.
a(n) = Sum_{k=0..n-1} (5 - n + k) * 5^k.
E.g.f.: exp(x)*(15*exp(4*x) + 4*x - 15)/16. - Stefano Spezia, May 28 2023
MATHEMATICA
LinearRecurrence[{7, -11, 5}, {4, 23, 117}, 23] (* Amiram Eldar, Apr 23 2022 *)
nxt[{n_, a_}] := {n + 1, 5 a + 4 - n}; NestList[nxt, {1, 4}, 30][[;; , 2]] (* Harvey P. Dale, Apr 28 2023 *)
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(x*(4-5*x)/((1-x)^2*(1-5*x)))
(PARI) a(n) = (3*5^(n+1)+4*n-15)/16;
(PARI) b(n, k) = sum(j=0, n-1, (k-n+j)*k^j);
a(n) = b(n, 5);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Apr 23 2022
STATUS
approved