A280240 Expansion of 1/(1 - Sum_{k>=1} x^(k+floor(1/2+sqrt(k)))).

1, 0, 1, 1, 1, 3, 3, 6, 9, 12, 22, 30, 49, 76, 113, 181, 271, 423, 653, 998, 1553, 2378, 3674, 5667, 8715, 13463, 20721, 31952, 49261, 75883, 117022, 180310, 277937, 428422, 660239, 1017760, 1568577, 2417700, 3726514, 5743524, 8852817, 13644751, 21030859, 32415319, 49961707, 77007095, 118691597

Offset

0,6

Comments

Number of compositions (ordered partitions) into nonsquares (A000037).

Links

Table of n, a(n) for n=0..46.

Index entries for sequences related to compositions

Formula

G.f.: 1/(1 - Sum_{k>=1} x^(k+floor(1/2+sqrt(k)))).

Example

a(5) = 3 because we have [2, 3], [3, 2] and [5].

Mathematica

nmax = 46; CoefficientList[Series[1/(1 - Sum[x^(k + Floor[1/2 + Sqrt[k]]), {k, 1, nmax}]), {x, 0, nmax}], x]

Crossrefs

Cf. A000037, A087153.

Sequence in context: A128012 A289143 A323451 * A058628 A035528 A341241

Adjacent sequences: A280237 A280238 A280239 * A280241 A280242 A280243

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 29 2016

Status

approved