A392355 a(n) = Sum_{k=0..floor(4*n/7)} binomial(k,4*n-7*k).

1, 0, 1, 0, 1, 0, 1, 1, 1, 5, 1, 15, 1, 35, 2, 70, 10, 126, 46, 210, 166, 331, 496, 508, 1288, 806, 3004, 1456, 6437, 3185, 12888, 8008, 24464, 20944, 44728, 53449, 80428, 129867, 146320, 299006, 278104, 654402, 564929, 1370019, 1225811, 2766141, 2778772

Offset

0,10

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,4,0,-6,0,4,1,-1).

Formula

G.f.: (1-x^2)^3 / ((1-x^2)^4 - x^7).

a(n) = 4*a(n-2) - 6*a(n-4) + 4*a(n-6) + a(n-7) - a(n-8).

a(2*n) = A373913(n).

a(n) = A390218(n) - A390218(n-2).

Mathematica

CoefficientList[Series[(1-x^2)^3/((1-x^2)^4-x^7), {x, 0, 60}], x] (* Vincenzo Librandi, Jan 08 2026 *)

Prog

(PARI) my(N=50, x='x+O('x^N)); Vec((1-x^2)^3/((1-x^2)^4-x^7))
(PARI) a(n) = sum(k=0, 4*n\7, binomial(k, 4*n-7*k)) \\ Bruce Nye, Mar 05 2026
(Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R! (1-x^2)^3 / ((1-x^2)^4 - x^7)); // Vincenzo Librandi, Jan 08 2026

Crossrefs

Cf. A392271, A392356.

Cf. A390039, A390218, A390219.

Cf. A373913.

Sequence in context: A295574 A087727 A390220 * A039807 A213590 A185263

Adjacent sequences: A392352 A392353 A392354 * A392356 A392357 A392358

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 08 2026

Status

approved