A392540 Expansion of 1 / ((1-x)^2 - x^5).

1, 2, 3, 4, 5, 7, 11, 18, 29, 45, 68, 102, 154, 235, 361, 555, 851, 1301, 1986, 3032, 4633, 7085, 10838, 16577, 25348, 38752, 59241, 90568, 138472, 211724, 323728, 494973, 756786, 1157071, 1769080, 2704817, 4135527, 6323023, 9667590, 14781237, 22599701, 34553692

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,1).

Formula

a(n) = Sum_{k=0..floor(n/5)} binomial(n-3*k+1,n-5*k).

a(n) = 2*a(n-1) - a(n-2) + a(n-5).

Prog

(PARI) my(N=50, x='x+O('x^N)); Vec(1/((1-x)^2-x^5))

Crossrefs

Cf. A003520, A049016, A390044.

Sequence in context: A343305 A346076 A339357 * A279065 A327325 A340252

Adjacent sequences: A392537 A392538 A392539 * A392541 A392542 A392543

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 15 2026

Status

approved